Page 165 - New Medley 5 Semester 1

Least/Lowest Common Multiple (LCM)

Think about the multiples of 6 and 9.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...

Multiples of 9: 9, 18, 27, 36, 45, 54,...

Common multiples of 6 and 9: 18, 36, 54, ...

The lowest common multiple of 6 and 9 is 18.

Thus, the LCM is the smallest number which is divisible by all the given

numbers.

There are three ways to find the LCM of the given numbers.

I. By using multiple and common multiple method

II. By the prime factorisation method

III. By the common division method

Let us understand these methods in the following examples.

Example 5: Find the LCM of 4 and 6 using the common multiple

method.

Solution: Multiples of 4 = 4, 8, 12 , 16, 20, 24 , 28, 32, 36 , ...

Multiples of 6 = 6, 12 , 18, 24 , 30, 36 , 42, ...

Common multiples of 4 and 6 = 12, 24, 36, ...

∴ LCM of 4 and 6 = 12

Example 6: Find the LCM of 12 and 18 using the prime factorisation

method.

Solution: 212 218
2 6 3 9

3 3 3 3
1 1

∴ 12 = 2 × 2 × 3 ∴ 18 = 2 × 3 × 3
(Two 2s and one 3) (One 2 and two 3s)

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