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example 2. Find the LCM of 12 and 18.

Solution. Multiples of 12 are 12, 24, 36, 48, 60, 72, ...
Multiples of 18 are 18, 36, 54, 72, 90, ...

Common multiples of 12 and 18 are 36, 72, ...

Thus, the Least Common Multiple (LCM) of 12 and 18 is 36.

example 3. Find the LCM of 15 and 24.

Solution. Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, ...

Multiples of 24 are 24, 48, 72, 96, 120, ...

Common multiples of 15 and 24 are 120, 240, ...

Thus, the Least Common Multiple (LCM) of 15 and 24 is 120. Tips

For listing the common multiples, find the first common
multiple and then write its multiples.
Exercise 3E

1. Write the common multiples of each pair of numbers and circle the lowest common
multiple.

a. 6, 10 b. 8, 12 c. 9, 21 d. 10, 16 e. 18, 20

2. Write the lCM of each pair of numbers in the circle.

a. 8 16 b. 3 6 c. 6 9 d. 10 15

3. Find the lCM of these numbers by the listing multiples method.
a. 8, 9 b. 18, 24 c. 15, 20 d. 12, 16

e. 24, 36 f. 15, 25 g. 15, 20, 30 h. 20, 30, 50
i. 20, 32, 40 j. 11, 22, 33 k. 12, 15, 40 l. 12, 16, 20

relATioNSHiP BeTWeeN HCF ANd lCM

The LCM and HCF of two numbers are related with the formula:

lCM × HCF = Product of the two numbers

If any three of them are known, we can find the fourth. This relationship between HCM
and LCM is useful for solving many problems.

78 Mathematics 5