What is the Least Common Multiple of 390 and 400?

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 390 and 400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 390 and 400, than apply into the LCM equation.

GCF(390,400) = 10
LCM(390,400) = ( 390 × 400) / 10
LCM(390,400) = 156000 / 10
LCM(390,400) = 15600

Least Common Multiple (LCM) of 390 and 400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 400. First we will calculate the prime factors of 390 and 400.

Prime Factorization of 390

Prime Factorization of 400

Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 400.

LCM(390,400) = 2⁴ × 3¹ × 5² × 13¹
LCM(390,400) = 15600