Lowest Common Multiple (LCM)

The smallest number that can be divided by the given numbers without leaving any remainder is called the LCM.

LCM by Prime factorisation method:

In this method, we first list the prime factors of the numbers and then multiply the common factors and the remaining prime factors.

Example : Find the LCM of 18 and 24.

Prime factorisation of 18 : 2 \times 3 \times 3

Prime factorisation of 24 : 2 \times 2 \times 2 \times 3

LCM = 2 \times 3 \times 3 \times 2 \times 2 = 72

LCM by Common Division method :

Step 1: Divide by the smallest prime number which can divide at least one of the numbers and bring down the numbers that cannot be divided further.

Step 2 : Continue division by the smallest possible prime numbers till the last row contains prime numbers or co-prime numbers.

Step 3 : Multiple all the factors and the numbers in the last row get LCM.

For example : Find the LCM of 12,16, 20.

LCM = 2 \times 2 \times 2 \times 2 \times 3 \times 5 = 240

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