What is the difference between the LCM and the HCF of the numbers 20, 30, and…

Prime factorizations:

• 20 = 2^2 × 5

• 30 = 2 × 3 × 5

• 40 = 2^3 × 5

LCM:

Take each prime at its highest power across the numbers: 2^3, 3^1, 5^1. So LCM = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 120.

HCF:

Take primes common to all numbers at their lowest powers: 2^1 and 5^1. So HCF = 2^1 × 5^1 = 2 × 5 = 10.

Difference:

LCM − HCF = 120 − 10 = 110. Therefore, the difference between the LCM and the HCF of 20, 30 and 40 is 110.