WORKED MATH ANSWER

HCF and LCM of 20 and 30

For 20 and 30, the highest common factor is 10 and the least common multiple is 60.

THE DIRECT ANSWER

HCF = 10. LCM = 60.

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

HIGHEST COMMON FACTOR10

10 divides both 20 and 30 exactly.

LEAST COMMON MULTIPLE60

60 is the first positive number both values divide into.

STEP 1 · LIST THE FACTORS

Factors of 20 and 30

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Common factors: 1, 2, 5, 10

The common factors are the values that divide both numbers with no remainder. The greatest one is 10, so HCF(20, 30) = 10.

STEP 2 · USE PRIME FACTORS

Prime factorisation working

20 =2² × 5

30 =2 × 3 × 5

For the HCF, use only the shared primes at their smallest powers: 2 × 5 = 10. For the LCM, use every prime needed at its greatest power: 2² × 5 × 3 = 60.

20 × 30 = 600 = 10 × 60

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 20 and 30. It is not a replacement for checking your own question: use the calculators above for other inputs.