# What is the Least Common Multiple of 8 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 8 and 21 is 168.

LCM(8,21) = 168

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## Least Common Multiple of 8 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 8 and 21, than apply into the LCM equation.

GCF(8,21) = 1
LCM(8,21) = ( 8 × 21) / 1
LCM(8,21) = 168 / 1
LCM(8,21) = 168

## Least Common Multiple (LCM) of 8 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 21. First we will calculate the prime factors of 8 and 21.

### Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 23

### 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 8 and 21.

LCM(8,21) = 23 × 31 × 71
LCM(8,21) = 168