# What is the Least Common Multiple of 21 and 34?

*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 21 and 34 is **714**.

LCM(21,34) = 714

## Least Common Multiple of 21 and 34 with GCF Formula

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 21 and 34, than apply into the LCM equation.

GCF(21,34) = 1

LCM(21,34) = ( 21 × 34) / 1

LCM(21,34) = 714 / 1

LCM(21,34) = 714

## Least Common Multiple (LCM) of 21 and 34 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 34. First we will calculate the **prime factors of 21 and 34**.

### Prime Factorization of 21

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

21 = 3^{1} × 7^{1}

### Prime Factorization of 34

Prime factors of 34 are 2, 17. Prime factorization of **34** in exponential form is:

34 = 2^{1} × 17^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 21 and 34**.

LCM(21,34) = 3^{1} × 7^{1} × 2^{1} × 17^{1}

LCM(21,34) = 714