What are the Highest common factor and Lowest common multiple of 6, 72, 120 ?

Method: factor each number into primes; HCF is the product of common primes with the smallest exponents, and LCM is the product of all primes with the largest exponents.

• 6 = 2 × 3

• 72 = 2 × 2 × 2 × 3 × 3 ( = 2^3 × 3^2 )

• 120 = 2 × 2 × 2 × 3 × 5 ( = 2^3 × 3 × 5 )

HCF calculation: common primes are 2 and 3 with minimum exponents 1 and 1 → HCF = 2 × 3 = 6

LCM calculation: take the highest exponents for each prime: 2^3, 3^2, 5^1 → LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360

Final answer: HCF = 6, LCM = 360