What is the Least Common Multiple of 378 and 390?

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 378 and 390 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 378 and 390, than apply into the LCM equation.

GCF(378,390) = 6
LCM(378,390) = ( 378 × 390) / 6
LCM(378,390) = 147420 / 6
LCM(378,390) = 24570

Least Common Multiple (LCM) of 378 and 390 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 378 and 390. First we will calculate the prime factors of 378 and 390.

Prime Factorization of 378

Prime Factorization of 390

Now multiplying the highest exponent prime factors to calculate the LCM of 378 and 390.

LCM(378,390) = 2¹ × 3³ × 7¹ × 5¹ × 13¹
LCM(378,390) = 24570