Question

Find the LCM of the following numbers by listing multiples

12,16. 15,20. 7,8. 3,4and6. 5,7and 10

Find the PCM of the following by prime factorisation method :-

24,60. 10,12,18. 12,48,60. 18,20,30,.
9,15,18,20

Find the PCM of the following by division method

18,36,60,72
20,25,30,50
48,56,105,225
8,12,20,30,80
9,12,18,24,27
22,54,108,135,198

Find the least number which is exactly divisible by 14,21,24and42

Answer 1

1) find the LCM of the following numbers by listing multiples
i)12, 16
12 = 2×2×3
16 = 2×2×2×2
LCM of 12 and 16 is 2×2×2×2×3 = 48

ii)15, 20
15 = 3×5
20 = 2×2×5
LCM of 15 and 20 is 2×3×5 = 30

iii)7, 8
7 = 1×7
8 = 1×2×2×2
LCM of 7 and 8 is 2×2×2×7 = 56

iv)3, 4 and 6
3 = 1×3
4=2×2
6=1×2×3
LCM of 3, 4 and 6 is 2×2×3 = 12

v)5, 7 and 10
5 = 1×5
7=1×7
10=2×5
LCM of 5, 7 and 10 is 2×5×7 = 70

2) LCM by prime factorisation of the following numbers

i)24, 60
24 = 2×2×2×3
60 = 2×2×3×5
LCM of 24, 60 is 2×2×2×3×5 = 120

ii)10, 12, 18
10=2×5
12=2×2×3
18=2×3×3
LCM of 10, 12, 18 is 2×2×3×3×5 = 180

iii)18, 20, 30
18=2×3×3
20=2×2×5
30=2×3×5
LCM of 18, 20, 30 is 2×2×3×3×5 = 180

iv)9, 15, 18, 20
9=3×3
15=3×5
18=2×3×3
20=2×2×5
LCM of 9, 15, 18, 20 is 2×2×3×3×5 = 180

3) Find LCM of the by division method

i)18,36,60,72
ii)20,25,30,50
iii)48,56,105,225
iv)8,12,20,30,80
v)9,12,18,24,27
vi)22,54,108,135,198

refer image file

4)find the least number which is exactly divisible by 14, 21, 24 and 42

14 = 2×7
21 = 3×7
24 = 2×2×2×3
42 = 2×3×7

LCM of 14, 21, 24, 42 is 2×2×2×3×7 = 168

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Answer 2

Step-by-step explanation: