Question

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

Answer 1

We have : 

6 = 2¹ × 3¹ and 20 = 2 × 2 × 5 = 2² × 5¹.

You can find HCF(6, 20) = 2 and LCM(6, 20) = 2 × 2 × 3 × 5 = 60, as done in your earlier classes.

Note that HCF(6, 20) = 2¹ = Product of the smallest power of each common prime factor in the numbers.

LCM (6, 20) = 2² × 3¹ × 5¹ = Product of the greatest power of each prime factor, involved in the numbers.

From the example above, you might have noticed that HCF(6, 20) × LCM(6, 20)

= 6 × 20. In fact, we can verify that for any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b. We can use this result to find the LCM of two positive integers, if we have already found the HCF of the two positive integers.