What is the Least Common Multiple of 342 and 357?

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 of 342 and 357 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 342 and 357, than apply into the LCM equation.

GCF(342,357) = 3
LCM(342,357) = ( 342 × 357) / 3
LCM(342,357) = 122094 / 3
LCM(342,357) = 40698

Least Common Multiple (LCM) of 342 and 357 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 342 and 357. First we will calculate the prime factors of 342 and 357.

Prime Factorization of 342

Prime Factorization of 357

Now multiplying the highest exponent prime factors to calculate the LCM of 342 and 357.

LCM(342,357) = 2¹ × 3² × 19¹ × 7¹ × 17¹
LCM(342,357) = 40698