HCF and LCM of 14 and 21
For 14 and 21, the highest common factor is 7 and the least common multiple is 42.
HCF = 7. LCM = 42.
These two results answer different questions: the HCF is the largest shared divisor, while the LCM is the smallest positive shared multiple.
7 divides both 14 and 21 exactly.
42 is the first positive number both values divide into.
Factors of 14 and 21
- Factors of 14
- 1, 2, 7, 14
- Factors of 21
- 1, 3, 7, 21
- Common factors
- 1, 7
The common factors are the values that divide both numbers with no remainder. The greatest one is 7, so HCF(14, 21) = 7.
Prime factorisation working
For the HCF, use only the shared primes at their smallest powers: 7 = 7. For the LCM, use every prime needed at its greatest power: 2 × 7 × 3 = 42.
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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 14 and 21. It is not a replacement for checking your own question: use the calculators above for other inputs.