# Least Common Multiple of 21 and 30

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 30 is 210.

LCM(21,30) = 210

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## Least Common Multiple of 21 and 30 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 30, than apply into the LCM equation.

GCF(21,30) = 3
LCM(21,30) = ( 21 × 30) / 3
LCM(21,30) = 630 / 3
LCM(21,30) = 210

## Least Common Multiple (LCM) of 21 and 30 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 30. First we will calculate the prime factors of 21 and 30.

### Prime Factorization of 21

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

21 = 31 × 71

### Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 21 × 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 21 and 30.

LCM(21,30) = 31 × 71 × 21 × 51
LCM(21,30) = 210

#### Related Least Common Multiples of 30

Guest 2020-06-13 03:12:49

By the way. I improved in this website and I got 98% in my LCM and GCF test!

Guest 2020-06-13 03:11:30

It would be nice if there were 3 number options... example 14, 18 and 63.

Guest 2020-06-13 03:09:47