Class 8: Factors and Multiples - Exercise 4C
1. Find the L.C.M. of the following numbers using common division method:
i.
24, 36, 40
Answer:
2
2
3
2
3
5
24
12
6
2
1
1
1
36
18
9
3
3
1
1
40
20
10
10
5
5
1
LCM = 2 x 2 x 3 x 2 x 3 x 5 = 360
ii.
15, 24, 30, 40
Answer:
3
5
2
2
2
15
5
1
1
1
1
24
8
8
4
2
1
30
10
2
1
1
1
40
40
8
4
2
1
12
4
4
2
1
1
1
1
15
5
5
5
5
5
5
1
18
6
2
1
1
1
1
1
24
8
8
4
2
1
1
1
LCM = 3 x 5 x 2 x 2 x 2 = 120
iii.
9, 12, 15, 18, 24, 56
Answer:
3
3
2
2
2
7
5
9
3
1
1
1
1
1
1
56
56
56
28
14
7
1
1
LMC = 3 x 3 x 2 x 2 x 7 x 5 = 2520
1
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iv.
22, 54, 108, 135, 198
Answer:
2
3
3
11
3
2
5
22
54
11
27
11
9
11
3
1
3
1
1
1
1
1
1
LCM = 2 x 3x 3 x 11 x 3 x 2 x 5 = 5940
v.
108
54
18
6
6
2
1
1
198
99
33
11
1
1
1
1
576, 672, 720
Answer:
2
2
2
2
3
3
2
2
5
7
576
672
288
336
144
168
72
84
36
42
12
14
4
14
2
7
1
7
1
7
1
1
LCM = 2 x2 x 2 x 2 x 3 x 3 x 2 x 2 x 5 x 7 = 20160
vi.
135
135
45
15
15
5
5
1
720
360
180
90
45
15
5
5
5
1
1
1620, 1728, 1890
Answer:
2
5
2
3
3
3
3
7
2
2
2
2
1620
810
162
81
27
9
3
1
1
1
1
1
11
1728
864
864
432
144
48
16
16
16
8
4
2
1
1890
945
189
189
63
21
7
7
1
1
1
1
1
2
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LCM = 2 x 5 x 2 x 3 x 3 x 3 x 3 x 7 x 2 x 2 x 2 x 2 = 181440
2. Use the prime factorization method to find the L.C.M. of the following numbers:
i.
72, 192, 240
Answer:
2
2
2
3
3
72
36
18
9
3
1
2
2
2
2
2
2
3
192
96
48
24
12
6
3
1
2
2
2
2
3
5
240
120
60
30
15
5
1
2
2
2
3
3
72
36
18
9
3
1
2
2
3
7
84
42
21
7
1
72 = 23 x 32
192 = 26 x 3
240 = 24 x 3 x 5
Hence LCM = 26 x 32 x 5 = 2880
ii.
56, 72, 84
Answer:
2
2
2
7
56
28
14
7
1
56 = 23 x 7
72 = 23 x 32
84 = 22 x 3 x 7
Hence LCM = 23 x 32 x 7 = 504
iii.
48, 72, 108, 144
Answer:
2
2
2
2
3
48
24
12
6
3
1
2
2
2
3
3
72
36
18
9
3
1
2
2
3
3
3
48 = 24 x 3
72 = 23 x 32
Hence LCM = 24 x 33 = 432
108
54
27
9
3
1
2
2
2
2
3
3
144
72
36
18
9
3
1
108 = 22 x 33
144 = 24 x 32
3
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iv.
168, 180, 330
Answer:
2
2
2
3
7
168
84
42
21
7
1
2
2
5
3
3
180
90
45
9
3
1
2
5
3
11
330
165
33
11
1
384
192
96
48
24
12
6
3
1
2
2
2
2
3
3
3
432
216
108
54
27
9
3
1
168 = 23 x 3 x 7
180 = 22 x 5 x 32
330 = 2 x 3 x 5 x 11
Hence LCM = 23 x 32 x 5 x 7 x 11 = 27720
v.
180, 384, 432
Answer:
2
2
5
3
3
180
90
45
9
3
1
2
2
2
2
2
2
2
3
180 = 22 x 5 x 32
384 = 27 x 3
432 = 24 x 33
Hence LCM = 27 x 33 x 5 = 17280
vi.
288, 432, 486
Answer:
2
2
5
3
3
180
90
45
9
3
1
2
2
2
2
2
2
2
3
384
192
96
48
24
12
6
3
1
2
2
2
2
3
3
3
432
216
108
54
27
9
3
1
180 = 22 x 5 x 32
384 = 27 x 3
432 = 24 x 33
Hence LCM = 27 x 5 x 33 =17280
4
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3. Find the H.C.F and L.C.M of the following:
i.
23 x 32 x 5, 22 x 33 x 5 and 24 x 3 x 53 x 7
ii.
22 x 3 x 52, 23 x 32 x 7 and 2 x 33 x 5 x 7
iii.
52 x 7 x 2, 5 x 7 x 32 and 22 x 3 x 11
iv.
22 x 33 x 54, 23 x 32 x 5 and 2 x 3 x 7 x 52
4. Find the H.C.F. and L.C.M of the following fractions:
i.
ii.
iii.
5 5 10
, ,
6 9 27
2 8 20 40
,
,
,
,
,
,
3 15 27 81
3 9 18 15
7 14 35 28
5. Find the smallest number exactly divisible by 28, 36, 42 and 54
6. Find the least number which when divided by 12, 16, 18, 21 and 28 leaves the same remainder 7 in each
case.
7. Find the least number which when diminished by 8, is divisible by each of the numbers 12, 15, 20 and
54.
8. Find the smallest number which when increased by 5 is divisible by each of the numbers 48, 60, 72 and
108.
9. Find the greatest number of four digits which is exactly divisible by each one of the numbers 12, 18, 21
and 28.
10. Five bells begin to toll together and toll respectively at intervals of 6,7,8,9 and 12 seconds. After how
much time would they toll together again?
11. Find the least perfect square number which is divisible by 3, 4, 5, 6 and 8.
12. Find the least number that should be added to 2500 so that the sum is divisible by each one of the
numbers 3, 4, 5 and 6.
13. Find the least number of five digits which is exactly divisible by each one of the numbers 12, 15 and 20.
14. Three boys start cycling around a circular park from the same point at the same time and in the same
direction. If these boys, each cycling at a constant speed, complete a round in 24 min, 36 min and 54
min respectively, then after what time would they meet again.
15. The product of two numbers is 16184 and their L.C.M. is 952. Find their H.C.F.
16. The product of two numbers is 591223 and their H.C.F. is 952. Find their L.C.M.
17. The H.C.F of two numbers is 14 and their L.C.M is 11592. If one number is 504, find the other.
18. The sum of the H.C.F and L.C.M of two numbers is 1150. If the L.C.M is 45 times the H.C.F. and one
of the numbers is 125, then find the other number.
19. The difference between the L.C.M. and H.C.F of two numbers is 294. If the L.C.M is 15 times the H.C.F
and one of the numbers is 105, find the other.
20. The product of two co-prime numbers is 6. What would be the L.C.M of these numbers?
5
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