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What is the Least Common Multiple of 5 and 21?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 5 and 21 is 105.

LCM(5,21) = 105

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Least Common Multiple of 5 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 21, than apply into the LCM equation.

GCF(5,21) = 1
LCM(5,21) = ( 5 × 21) / 1
LCM(5,21) = 105 / 1
LCM(5,21) = 105

Least Common Multiple (LCM) of 5 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 21. First we will calculate the prime factors of 5 and 21.

Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 51

Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:

21 = 31 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 21.

LCM(5,21) = 51 × 31 × 71
LCM(5,21) = 105

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