Question

Find L.C. M and G. C.D. of 540 and 2592 by prime factorisation method?

Answer 1

Let us first find the prime factors of the two given numbers:

540 = 2 × 2 × 3 × 3 × 3 × 5 = 2 ^2  x  3^3  x  5

2592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3  = 2^5  x 3^4

LCM is given by  product of all prime factors excluding the common/repeating factors.

So, LCM = 2^5  x  3^4  x 5 = 12960

LCM = 12960

GCD is given by product of common/repeating prime factors for both given numbers. (underlined for easy identification)

So, GCD is 2 × 2 × 3 × 3 × 3 = 108

GCD = 108