WORKED MATH ANSWER

HCF and LCM of 8 and 12

For 8 and 12, the highest common factor is 4 and the least common multiple is 24.

THE DIRECT ANSWER

HCF = 4. LCM = 24.

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

HIGHEST COMMON FACTOR4

4 divides both 8 and 12 exactly.

LEAST COMMON MULTIPLE24

24 is the first positive number both values divide into.

STEP 1 · LIST THE FACTORS

Factors of 8 and 12

Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors: 1, 2, 4

The common factors are the values that divide both numbers with no remainder. The greatest one is 4, so HCF(8, 12) = 4.

STEP 2 · USE PRIME FACTORS

Prime factorisation working

8 =2³

12 =2² × 3

For the HCF, use only the shared primes at their smallest powers: 2² = 4. For the LCM, use every prime needed at its greatest power: 2³ × 3 = 24.

8 × 12 = 96 = 4 × 24

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 8 and 12. It is not a replacement for checking your own question: use the calculators above for other inputs.