HCF of two or more
than two numbers is the greatest number that divides each of them exactly.
The Least number which
is exactly divisible by each one of the given numbers is called LCM
HCF of fractions =
HCF of Numerators / LCM of Denominators
LCM of fractions =
LCM of Numerators / HCF of Denominators
HCF of Numbers x
LCM of Numbers = Product of Numbers
1
Find the HCF of 144 and
192?
a) 27 b)
35 c) 48 d) 25
144/ 192 /1
144
48/
144 /3
144
0
HCF of 144, 192 is 48
Or
144 = 24 x 32
192 = 26 x 3
HCF of 144, 192 is 48 (24 x 3)
2/144
2/72 2/ 36 2/ 18 
3/ 9
3
2/192 2/96 2/ 48 2/ 24
2/ 12
2/ 6
3
2
Find the HCF of 144, 180
and 192?
a) 27 b)
35 c) 12 d) 25
144/ 192 /1
144
48/
144 /3
144
0
48/ 180
/3
144
36/ 48 /1 36
12/ 36 /3
36
0
HCF of 144, 180 and 192 is 12
Or
144 = 24 x 32
180 = 22 x 32 x 5
192 = 26 x 3
HCF of 144, 180 and 192 is 12 (22 x 3)
2/144 2/72 2/ 36 2/ 18
3/ 9
3
2/180 2/90 2/ 45 3/ 15
5
2/192 2/96 2/ 48 2/ 24
2/ 12
2/ 6
3
3
Find the HCF of 876,
492, 1824 and 1960?
a) 12 b)
36 c) 4 d) 8
492/ 876 /1
492
384/ 492 /1
384
108/ 384 /3
324
60/ 108 / 1
60
48/ 60 /1
48
12/ 48 / 4
48
0
12/ 1824
/152
1824
0
12/ 1960 /163
1956
4/
12 /3
12
0
HCF of 876, 492, 1824 and 1960 is 4
Or
876 = 22 x 3 x 73
492 = 22 x 3 x 41
1824 = 25 x 3 x 19
1960 = 23 x 5 x 72
HCF of 876, 492, 1824 and 1960 is 4 (22)
2/876 2/438 3/ 219
73
2/492 2/246 3/ 123
41
2/1824 2/912 2/ 456 2/ 228
2/ 114
3/ 57
19
2/1960 2/980 2/ 490 5/ 245
7/ 49
7
4
Two vats contain
respectively 540 and 720 liters, find the vessel of greatest capacity that will
empty off both vats.
a) 90 liters b)
160 liters c) 180 liters d) 80 liters
540/ 720 /1
540
180/
540 /3
540
0
Greatest capacity that will empty off both vats is 180 liters.
Or
540 = 22 x 33 x 5
720 = 24 x 32 x 5
HCF of 540 and 720 is 180 (22 x 32 x 5)
2/540 2/270 3/ 135 3/ 45
3/ 15
5
2/720 2/360 2/ 180 2/ 90
3/ 45
3/ 15
5
5
Two masses of gold
weighing 44270 and 72190 grams respectively are each to be made into coins of
the same size, what is the weight of the largest possible coin?
a) 90 gm b)
110 gm c) 10 gm d) 210 gm
44270 = 2 x 5 x 4427
72190 = 2 x 5 x 7219
HCF of 44270 and 72190 is 10 gm
2│44270
5│22135
4427
2│721905│36095
7219
6
Find the greatest weight
which can be contained exactly in 1 kg 235 gm and 3 kg 430 gm?
a) 10 gm b) 5 gm c) 15 gm d)
20 gm
1 kg 235 gm = 1235 gm = 5 x 13 x 19
3 kg 430 gm = 3430 gm = 2 x 5 x 73
HCF is 5 gm
7
Find the greatest weight
which can be contained exactly in 6 kg 7 hg 4 dag 3 gm and 9 kg 9 dag 7 gm?
a) 10 gm b) 11 gm c) 15 gm d)
12 gm
6 kg 7 gh 4 dsg 3 gm =
6743 gm = 11 x 613
9 kg 9 dag 7 gm = 9097 gm = 11 x 827
HCF is 11 gm
8
Find the greatest
measure which is exactly contained in 10 liters 857 milliliters and 15 liters 87
milliliters?
a) 140 ml b)
138 ml c) 141 ml d) 142 ml
10 lit 857 ml = 10857 ml = 3 x 7 x 11 x 47
15 lit 087 ml = 15087 ml = 3 x 17 x 47
HCF is 141 (3 x 47)
9
What is the greatest length
which can be used to measure exactly 3 m 60 cm, 6 m, 8 m 40 cm and 18 m?
a) 1 m 10 cm b) 1 m 20 cm c) 105 cm d) 125 cm
3 m 60 cm = 360 cm = 23 x 32 x 5
6 m = 600 cm = 23 x 3 x 52
8 m 40 cm = 840 cm = 23 x 3 x 5 x 7
18 m = 1800 cm = 23 x 32
x 52
HCF is 120 cm (23 x 3 x 5)
10
What is the largest sum
of money which will divided Rs 12.90 and Rs 9.30 exactly?
a) Rs 1.30 b) 30 Paisa c) Rs 3 d) Rs 2
Rs 12.90 = 1290 Paisa = 2 x 3 x 5 x 43
Rs 9.30 = 930 Paisa = 2 x 3 x 5 x 31
HCF is 30 Paisa (2 x 3 x 5)
11
Find the HCF of 16.50,
0.45 and 15?
a) 0.10 b) 0.15 c) 0.20 d)
0.05
16.50 = 1650 = 2 x 3 x 52 x 11
0.45 = 0045 = 32
x 5
15 = 1500 = 22
x 3 x 53
HCF of 1650, 45, and 1500 is 15 (3 x 5)
So HCF of 16.50, 0.45, and 15 is 0.15
12
Find the HCF of 2.8,
0.98, 42, 0.161, and 0.0189?
a) 0.7 b)
0.007 c) 0.0007 d) 0.09
2.8 = 28000 = 22
x 53 x 7
0.98 = 9800 = 23
x 52 x 72
42 = 420000 = 25
x 3 x 54 x 7
0.161 = 1610 = 2 x 5 x 7
x 23
0.0189 = 189 = 33 x 7
HCF of 28000, 9800, 420000, 1610 and 189 is 7
So HCF of 2.8, 0.98, 420000, 0.161 and 0.0189 is 0.0007
13
Find the HCF of 11.52, 12.96,
14.4, 15.84, and 17.28?
a) 3.43 b)
2.25 c) 1.44 d) 1.96
11.52 = 1152 = 27 x 32
12.96 = 1296 = 24 x 34
14.4 = 1440 = 25
x 32 x 5
15.84 = 1584 = 24 x 32 x 11
17.28 = 1728 = 26 x 32
HCF of 1152, 1296, 1440, 1584 and 1728 is 144 (24 x 32)
So HCF of 11.52, 12.96, 14.40, 15.84 and 17.28 is 1.44
14
Find the LCM of 40, 36
and 126?
a) 2220 b) 2520 c) 2020 d)
2525
36 = 22 x 32
40 = 23 x 5
126 = 2 x 32 x 7
LCM of 36, 40 and 126 is 2520 (23 x 32 x 5
x 7)
Or
2/ 36, 40,
1262/18, 20, 63
3/
9, 10,
63
3/3,
10, 21 5/1,
10, 7
1, 2,
7
2 x 2 x 2 x 3 x 3 x 5 x 7
23 x 32 x 5 x 7
LCM of 36, 40 and 126 is 2520 (23 x 32 x 5
x 7)
15
Find the LCM of 84, 90
and 120?
a) 2220 b) 2520 c) 2020 d)
2525
84 = 22 x 3 x 7
90 = 2 x 32 x 5
120 = 23 x 3 x 5
LCM of 84, 90 and 120 is 2520 (23 x 32 x 5
x 7)
Or
2/ 84,
90, 1202/42, 45, 603/21, 45, 30 5/7,
15, 10
7, 3,
2
2 x 2 x 2 x 3 x 3 x 5 x 7
23 x 32 x 5 x 7
LCM of 84, 90 and 120 is 2520 (23 x 32 x 5
x 7)
16
Find the LCM of 12, 15,
24, 52, 55, 60, 77 and 210?
a) 122120 b) 120120 c) 12020 d)
125125
12 = 22 x 3
15 = 3 x 5
24 = 23 x 3
52 = 22 x 13
55 = 5 x 11
60 = 22 x 3 x 5
77 = 7 x 11
210 = 2 x 3 x 5 x 7
LCM of 12, 15, 24, 52, 55, 60, 77 and 210 is 120120 (23x3x5x7x11x13)
Or
2/12,
15, 24, 52, 55, 60, 77, 210
2/
6, 15, 12, 26, 55, 30, 77, 105
3/
3, 15,
6, 13, 55, 15, 77, 105
5/ 1,
5, 2, 13, 55,
5, 77, 35 
11/1, 1, 2, 13,
11, 1,
77, 7
7 /1,
1, 2, 13,
1, 1, 7, 7
1, 1,
2, 13, 1,
1, 1, 1
2 x 2 x 2 x 3 x 5 x 7 x 11 x 13
23 x 3 x 5 x 7 x 11 x 13
LCM of 12, 15, 24, 52, 55, 60, 77 and 210 is 120120
17
Find the LCM of 3, 1.2 and
0.06?
a) 10 b) 6 c) 0.8 d)
1.2
3 = 300 = 22 x 3 x 52
1.2 = 120 = 23 x 3 x 5
0.06 = 6 = 2 x 3
LCM of 300, 120, and 6 is 600 (23 x 3 x 52)
So LCM of 3, 1.2 and 0.06 is 6
18
Find the LCM of 1.2,
0.24 and 6?
a) 10 b) 6 c) 8 d)
12
1.2 = 120 = 23 x 3 x 5
0.24 = 24 = 23 x 3
6 = 600 = 23 x 3 x 52
LCM of 120, 24 and 6 is 600 (23 x 3 x 52)
So LCM of 1.2, 0.24 and 6 is 6
19
Find the LCM of 20, 2.8
and 0.25?
a) 100 b) 140 c) 80 d)
120
20 = 2000 = 24 x 53
2.8 = 280 = 23 x 5 x 7
0.25 = 25 = 52
LCM of 2000, 280 and 25 is 14000 (24 x 53
x 7)
So LCM of 20, 2.8 and 0.25 is 140
20
Find the HCF of 3/4, 5/6
and 6/7?
a) 1/81 b)
81 c) 1/84 d) 84
HCF of 3, 5 and 6 is 1
And LCM of 4, 6 and 7 is 84
So HCF of 3/4, 5/6 and 6/7 is 1/84
21
Find the HCF of 6/8, 2
1/2 and 15/16?
a) 1/21 b)
16 c) 1/16 d) 21
6/8, 5/2 and 15/16
HCF of 6, 5 and 15 is 1
And LCM of 8, 2 and 16 is 16
So HCF of 6/8, 2 1/2 and 15/16 is 1/16
22
What is the greatest
length which is contained a whole number of times exactly in both 7 ½ meters
and 4 ¼ meters?
a) 26 cm b) 25 cm c) 80 cm d)
30 cm
15/2 and 17/4
HCF of 15 and 17 are 1
LCM of 2 and 4 is 4
¼ meters (or 25 cm)
23
Find the LCM of 8, 16/20
and 10/7?
a) 1/80 b) 80 c) 1/89 d)
89
8/1, 16/20 and 10/7
LCM of 8, 16 and 10 is 80
HCF of 1, 20 and 7 is 1
So, LCM of 8, 16/20 and 1 3/7 is 80 (80/1)
24
Find the LCM of 6/8, 2 ½
and 15/16?
a) 1/80 b) 80 c) 1/89 d)
89
6/8, 5/2 and 15/16
LCM of 6, 5 and 15 is 30
HCF of 8, 2 and 16 is 2
So, LCM of 6/8, 2 ½ and 15/16 is 15 (30/2)
25
Find the least number
which, when divided by each of the fractions 4/5, 3/10 and 12/35 gives a whole
number as quotient in each case?
a) 3.60 b) 2.40 c) 2.60 d)
3.40
LCM of 4, 3 and 12 is 12
HCF of 5, 10 and 35 is 5
So, LCM of 4/5, 310 and 12/35 is 2.40 (12/5)
26
The LCM of two numbers
is 64699, their HCF is 97 and one of the numbers is 2231. Find other?
a) 2183 b) 2813 c) 2831 d)
2381
HCF of Numbers x LCM of Numbers = Product of Numbers
97 x 64699 = 2231 x Other Number
Other Number is 2831
27
The LCM of two numbers
is 11781, their HCF is 119 and one of the numbers is 1071. Find other?
a) 1830 b) 1309 c) 2831 d)
2381
HCF of Numbers x LCM of Numbers = Product of Numbers
119 x 11781 = 1071 x Other Number
Other Number is 1309
28
The product of two numbers is 20736 and their
HCF is 54. Find their LCM?
a) 484 b) 384 c) 348 d) 364
HCF of Numbers x LCM of Numbers = Product of Numbers
54 x LCM = 20736
LCM is 384
29
The product of two
numbers is 396 x 576 and their LCM is 6336. Find their HCF?
a) 48 b) 36 c) 38 d) 34
HCF of Numbers x LCM of Numbers = Product of Numbers
HCF x 6336 = 396 X 576
HCF is 36
30
What is the greatest
number that will exactly divide 96, 528 and 729?
a) 12 b)
48 c) 36 d) 3
96 = 25 x 3
528 = 24 x 3 x 11
729 = 36
HCF of 96, 528 and 729 is 3 (31)
31
What is the greatest
number that will exactly divide 370 and 592?
a) 47 b)
48 c) 36 d) 74
370 = 2 x 5 x 37
592 = 24 x 37
HCF of 370 and 592 is 74 (2 x 37)
32
What is the greatest number
that will exactly divide 312, 351 and 650?
a) 39 b)
52 c) 26 d) 13
312 = 23 x 3 x 13
351 = 33 x 13
650 = 2 x 52 x 13
HCF of 312, 351 and 650 is 13
33
What is the greatest number
that will divided 38, 45 and 52 and leaves as remainders 2, 3 and 4
respectively?
a) 8 b)
10 c) 6 d) 12
38, 45 and 52
38 – 2, 45 -3, and 52 – 4
36, 42 and 48
HCF of 36, 42 and 48 is 6
34
What is the greatest number
that will divided 728 and 900 and leaves as remainders 8 and 4 respectively?
a) 20 b)
10 c) 16 d) 12
728 and 900
728 – 8 and 900 – 4
720 and 896
HCF of 720 and 896 is 16
35
What is the greatest number
that will divided 2930 and 3250 and leaves as remainders 7 and 11 respectively?
a) 69 b)
97 c) 79 d) 96
2930 and 3250
2930 – 7 and 3250 – 11
2923 and 3239
HCF of 2923 and 3239 is 79
36
Find the least number which
is divisible by 72, 90 and 120?
a) 260 b)
630 c) 360 d) 620
LCM of 72 (23 x 32), 90 (2 x 32
x 5), and 120 (23 x 3 x 5) is 360 (23 x 32 x5)
Or
2/ 72,
90, 1202/36, 45, 602/18, 45, 30 3/9,
45, 15 3/3,
15, 5
5/1,
5, 5
1, 1,
1
2 x 2 x 2 x 3 x 3 x5
23 x 32 x5
37
Find the least number
which is exactly divisible by 15, 55 and 99?
a) 485 b)
435 c) 495 d) 395
LCM of 15 (3 x 5), 55 (5 x 11), and 99 (32 x 11) is
495 (32 x 5 x 11)
38
Find the greatest number
less than 900, which is divisible by 8, 12 and 28?
a) 780 b)
735 c) 840 d) 895
LCM of 8 (23), 12 (22 x 3), and 28 (22
x 7) is 168 (23 x 3 x 7)
But 900 > 840 (168 x 5)
39
What is the least number
which when lessened by 5 is divisible by 36, 48, 21 and 28?
a) 1008 b)
1003 c) 1013 d) 1023
LCM of 36 (22 x 32), 48 (24 x
3), 21 (3 x 7) and 28 (22 x7) is 1013 (24x32x7)
1008 + 5 = 1013
40
Find the least number
which when divided by 24, 32 and 36 leaves the remainders 19, 27 and 31
respectively?
a) 823 b) 283 c) 382 d)
238
LCM of 24 (23 x 3), 32 (25) and 36 (22
x 32) is 288 (25 x 32)
24 – 19 = 5
32 – 27 = 5
36 – 31 = 5
288 – 5 = 283
41
Find the greatest number
of five digits which being divided by 56, 72, 84 and 96 leaves 50, 66, 78 and
90 as remainders respectively?
a) 97887 b)
97878 c) 98778 d) 97788
LCM of 56 (23 x 7), 72 (23 x 32),
84 (22 x 3 x 7) and 96 (25 x 3) is 2016 (25x32x7)
Greatest of five digit number is 98784 (2016 x 49)
56 – 50 = 6
72 – 66 = 6
84 – 78 = 6
96 – 90 = 6
98784 – 6 = 98778
42
Find the least number which
when divided by 24 and 36 will leave the remainders 14 and 26 respectively?
a) 64 b) 62 c) 59 d)
63
LCM of 24 (23 x 3) and 36 (22 x 32)
is 72 (23 x 32)
24 - 10 = 10
36 – 26 = 10
72 – 10 = 62
43
Find the least number which
when divided by 12, 21 and 35 will leave in each case the same remainder 6?
a) 326 b) 426 c) 536 d)
436
LCM of 12 (22 x 3), 21 (3 x 7), and 35 (5 x 7) is 420
(22 x 3 x 5 x7)
420 + 6 = 426
44
Find the least number which
when divided by 18, 24, 30 and 42 will leave in each case the same remainder 1?
a) 2526 b) 2521 c) 2520 d)
2550
LCM of 18 (2x32), 24 (23x3), 30 (2x3x5)
and 42 (2x3x7) is 2520 (23x32x5x7)
2520 + 1 = 2521
45
Find the least number
which when divided by 98 and 105 will leave in each case the same remainder 10?
a) 1326 b) 1480 c) 1536 d)
1436
LCM of 98 (2 x 72) and 105 (3 x5 x 7) is 1470 (2 x 3
x 5 x 72)
4170 + 10 = 1480
46
Find the greatest number
which will divided 410, 751 and 1030 so as to leave the remainder 7 in each
case?
a) 63 b) 31 c) 13 d)
36
410 – 7 = 403
751 – 7 = 744
1030 – 7 = 1023
HCF of 403 (13 x 31), 744 (23 x 3 x 31) and 1023 (3 x
11 x31) is 31
47
Find the greatest number
which will divided 260, 720 and 1410 so as to leave the remainder 7 in each
case?
a) 63 b)
31 c) 23 d) 36
260 – 7 = 253
720 – 7 = 713
1410 – 7 = 1403
HCF of 253 (11 x 23), 713 (23 x 31) and 1403 (23 x 61) is 23
48
Find the greatest number
which will divided 261, 933 and 1381 so as to leave the remainder 5 in each
case?
a) 63 b)
31 c) 32 d) 36
261 – 5 = 256
933 – 5 = 928
1381 – 5 = 1376
HCF of 256 (28), 928 (25 x 29) and 1376 (25
x 43) is 32
49
Find the greatest number
which is such that when 76, 151 and 226 are divided by it, the remainders are
all alike.
a) 65 b) 75 c) 57 d)
56
│76 -151│ = 75
│151 - 226│ = 75
│226 -76│ = 150
HCF of 75, 75 and 150 is 75
50
Find the greatest number
which is such that when 1305, 4665 and 6905 are divided by it, the remainders
are all alike.
a) 1165 b) 1120 c) 1157 d)
1156
│1305 -4665│ = 3360
│4665 - 6905│ = 2240
│6905 -1305│ = 5600
HCF of 3360 (25x3x5x7), 2240
(26x5x7) and 5600 (25x52x7) is
1120 (25x5x7)
51
Find the greatest number
which is such that when 705, 1805 and 1475 are divided by it, the remainders are
all alike.
a) 115 b) 110 c) 117 d)
156
│705 -1805│ = 1100
│1805 - 1475│ = 330
│1475 -705│ = 770
HCF of 1100 (22x52x11), 330 (2x3x5x11) and
770 (2x5x7x11) is 110 (2x5x11)
52
Find the greatest 3-digit
number of three digits which, when divided by 3, 4 and 5 leaves no remainder.
a) 690 b)
860 c) 960 d) 680
LCM of 3, 4 and 5 is 60
Pickup any option that greatest of three digit number and
divisible by 60
960 is divisible by 60 (960/60 =16)
53
Find the greatest of
3-digit number such that when divided by 3, 4 and 5, it leaves remainder 2 in
each case.
a) 122 b) 962 c) 958 d)
118
LCM of 3, 4 and 5 is 60
Pickup any option that greatest of three digit number and
subtract 2 and divisible by 60
962 – 2 = 960
960 is divisible by 60 (960/60 =16)
54
The greatest number of
four digits which is divisible by each one of the numbers 12, 18, 21 and 28 is:
a) 9848 b)
9864 c) 9828 d) 9636
LCM of 12, 18, 21 and 28 is 252 (4 x 9 x 7)
Pickup any option that greatest of four digit number and
divisible by 252 or 4 x 9 x 7
9828 is divisible by 4 x 9 x 7
55
Find the smallest three digit
number, such that they are exactly divisible by 3, 4, and 5?
a) 105 b) 120 c) 115 d)
130
LCM of 3, 4 and 5 is 60 (3 x 4 x 5)
Pickup any option that smallest of three digit number and
divisible by 60 or 3 x 4 x 5
120 is divisible by 3 x 4 x 5
56
Find the smallest three
digit number, such that when divided by 3, 4, and 5, it leaves remainder 2 in
each case?
a) 118 b)
120 c) 122 d) 132
LCM of 3, 4 and 5 is 60 (3 x 4 x 5)
Pickup any option that smallest of three digit number and
subtract 2 and divisible by 60 or 3 x 4 x 5
122 – 2 = 120
120 is divisible by 3 x 4 x 5
57
The least number of four
digits which is divisible by each one of the numbers 12, 18, 21 and 28 is:
a) 1090 b)
1006 c) 1008 d) 1080
LCM of 12, 15, 21 and 28 is 420 (3 x 4 x 5 x 7)
Pickup any option that smallest of four digit number and
divisible by 420 or 3 x 4 x 5 x 7
1008 is divisible by 3 x 4 x 5 x 7
58
Find the least number which
on being divided by 5, 6, 8, 9 and 12 leaves in each case a remainder 1, but
when divided by 13 leaves no remainder.
a) 3660 b)
3606 c) 3601 d) 3610
Pickup any option that smallest number and divisible by 13
3601 is divisible by 13
59
Find the least number
which on being divided by 2, 3, 4, 5 and 6 leaves in each case a remainder 1,
but when divided by 7 leaves no remainder.
a) 360 b)
306 c) 301 d) 310
Pickup any option that smallest number and divisible by 7
301 is divisible by 7
60
Find the least number
which on being divided by 3, 5, 6, 8, 10 and 12 leaves in each case a remainder
2, but when divided by 13 leaves no remainder.
a) 960 b)
606 c) 962 d) 310
Pickup any option that smallest number and divisible by 13
962 is divisible by 13
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