What is the Least Common Multiple of 324 and 342?

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 324 and 342 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 324 and 342, than apply into the LCM equation.

GCF(324,342) = 18
LCM(324,342) = ( 324 × 342) / 18
LCM(324,342) = 110808 / 18
LCM(324,342) = 6156

Least Common Multiple (LCM) of 324 and 342 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 324 and 342. First we will calculate the prime factors of 324 and 342.

Prime Factorization of 324

Prime Factorization of 342

Now multiplying the highest exponent prime factors to calculate the LCM of 324 and 342.

LCM(324,342) = 2² × 3⁴ × 19¹
LCM(324,342) = 6156