WORKED MATH ANSWER

HCF and LCM of 24 and 36

For 24 and 36, the highest common factor is 12 and the least common multiple is 72.

THE DIRECT ANSWER

HCF = 12. LCM = 72.

These two results answer different questions: the HCF is the largest shared divisor, while the LCM is the smallest positive shared multiple.

HIGHEST COMMON FACTOR12

12 divides both 24 and 36 exactly.

LEAST COMMON MULTIPLE72

72 is the first positive number both values divide into.

STEP 1 · LIST THE FACTORS

Factors of 24 and 36

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12

The common factors are the values that divide both numbers with no remainder. The greatest one is 12, so HCF(24, 36) = 12.

STEP 2 · USE PRIME FACTORS

Prime factorisation working

24 =2³ × 3

36 =2² × 3²

For the HCF, use only the shared primes at their smallest powers: 2² × 3 = 12. For the LCM, use every prime needed at its greatest power: 2³ × 3² = 72.

24 × 36 = 864 = 12 × 72

TRY ANOTHER PAIR

Need to calculate different numbers?

Enter any valid pair or longer list in the full calculators. They update as you type and show their own working.

Open HCF Calculator Open LCM Calculator

What these answers mean

Use the HCF when you want the largest equal grouping size or to simplify a fraction. Use the LCM when you want the first time two repeating schedules meet, or a least common denominator for fractions.

This page is a worked answer for 24 and 36. It is not a replacement for checking your own question: use the calculators above for other inputs.