# What is the Least Common Multiple of 198 and 212?

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 198 and 212 is 20988.

LCM(198,212) = 20988

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## Least Common Multiple of 198 and 212 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 198 and 212, than apply into the LCM equation.

GCF(198,212) = 2
LCM(198,212) = ( 198 × 212) / 2
LCM(198,212) = 41976 / 2
LCM(198,212) = 20988

## Least Common Multiple (LCM) of 198 and 212 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 212. First we will calculate the prime factors of 198 and 212.

### Prime Factorization of 198

Prime factors of 198 are 2, 3, 11. Prime factorization of 198 in exponential form is:

198 = 21 × 32 × 111

### Prime Factorization of 212

Prime factors of 212 are 2, 53. Prime factorization of 212 in exponential form is:

212 = 22 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 212.

LCM(198,212) = 22 × 32 × 111 × 531
LCM(198,212) = 20988