Find the HCF and LCM of 6, 72 and 120

• Numbers (C10)

Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.

Solution

Prime factorisation of numbers:

6 = 2 × 3

72 = 2³ × 3²

120 = 2³ × 3 × 5

Here, 2¹ and 3¹ are the smallest powers of the common factors 2 and 3, respectively.

So, HCF (6, 72, 120) = 2¹ × 3¹ = 2 × 3 = 6

2³, 3² and 5¹ are the greatest powers of the prime factors 2, 3 and 5 respectively involved in the three numbers.

So, LCM (6, 72, 120) = 2³ × 3² × 5¹ = 360