What is the Least Common Multiple of 360 and 378?

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 360 and 378 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 360 and 378, than apply into the LCM equation.

GCF(360,378) = 18
LCM(360,378) = ( 360 × 378) / 18
LCM(360,378) = 136080 / 18
LCM(360,378) = 7560

Least Common Multiple (LCM) of 360 and 378 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 378. First we will calculate the prime factors of 360 and 378.

Prime Factorization of 360

Prime Factorization of 378

Now multiplying the highest exponent prime factors to calculate the LCM of 360 and 378.

LCM(360,378) = 2³ × 3³ × 5¹ × 7¹
LCM(360,378) = 7560