What is the Least Common Multiple of 54 and 336?

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 54 and 336 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 336, than apply into the LCM equation.

GCF(54,336) = 6
LCM(54,336) = ( 54 × 336) / 6
LCM(54,336) = 18144 / 6
LCM(54,336) = 3024

Least Common Multiple (LCM) of 54 and 336 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 336. First we will calculate the prime factors of 54 and 336.

Prime Factorization of 54

Prime Factorization of 336

Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 336.

LCM(54,336) = 2⁴ × 3³ × 7¹
LCM(54,336) = 3024