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Question

Compute the LCM of 30 and 12 using prime factor method.

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Solution

Using the prime factor method to find L.C.M:

Express the given numbers as a product of prime factors as follows:

30=2×3×5

12=2×2×3

L.C.M = Product of all prime factors with highest number of instances of each factor.

Here, the prime factors are 2, 3 and 5.
3 and 5 occur once in the prime factorisation, while 2 occurs twice. Therfore, we multiply : ( 2 × 2 ) × 3 × 5

Required L.C.M = 2×2 × 3 × 5 = 60


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