WORKED MATH ANSWER

HCF and LCM of 15 and 35

For 15 and 35, the highest common factor is 5 and the least common multiple is 105.

THE DIRECT ANSWER

HCF = 5. LCM = 105.

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

HIGHEST COMMON FACTOR5

5 divides both 15 and 35 exactly.

LEAST COMMON MULTIPLE105

105 is the first positive number both values divide into.

STEP 1 · LIST THE FACTORS

Factors of 15 and 35

Factors of 15: 1, 3, 5, 15
Factors of 35: 1, 5, 7, 35
Common factors: 1, 5

The common factors are the values that divide both numbers with no remainder. The greatest one is 5, so HCF(15, 35) = 5.

STEP 2 · USE PRIME FACTORS

Prime factorisation working

15 =3 × 5

35 =5 × 7

For the HCF, use only the shared primes at their smallest powers: 5 = 5. For the LCM, use every prime needed at its greatest power: 3 × 5 × 7 = 105.

15 × 35 = 525 = 5 × 105

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.

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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 15 and 35. It is not a replacement for checking your own question: use the calculators above for other inputs.