# What is the Least Common Multiple of 198 and 214?

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 214 is 21186.

LCM(198,214) = 21186

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## Least Common Multiple of 198 and 214 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 214, than apply into the LCM equation.

GCF(198,214) = 2
LCM(198,214) = ( 198 × 214) / 2
LCM(198,214) = 42372 / 2
LCM(198,214) = 21186

## Least Common Multiple (LCM) of 198 and 214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 198 and 214. First we will calculate the prime factors of 198 and 214.

### 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 214

Prime factors of 214 are 2, 107. Prime factorization of 214 in exponential form is:

214 = 21 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 198 and 214.

LCM(198,214) = 21 × 32 × 111 × 1071
LCM(198,214) = 21186