# What is the Least Common Multiple of 6 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 6 and 21 is 42.

LCM(6,21) = 42

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## Least Common Multiple of 6 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 6 and 21, than apply into the LCM equation.

GCF(6,21) = 3
LCM(6,21) = ( 6 × 21) / 3
LCM(6,21) = 126 / 3
LCM(6,21) = 42

## Least Common Multiple (LCM) of 6 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 21. First we will calculate the prime factors of 6 and 21.

### Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 21 × 31

### 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 6 and 21.

LCM(6,21) = 21 × 31 × 71
LCM(6,21) = 42