What is the Least Common Multiple of 660 and 678?

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 660 and 678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 660 and 678, than apply into the LCM equation.

GCF(660,678) = 6
LCM(660,678) = ( 660 × 678) / 6
LCM(660,678) = 447480 / 6
LCM(660,678) = 74580

Least Common Multiple (LCM) of 660 and 678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 660 and 678. First we will calculate the prime factors of 660 and 678.

Prime Factorization of 660

Prime Factorization of 678

Now multiplying the highest exponent prime factors to calculate the LCM of 660 and 678.

LCM(660,678) = 2² × 3¹ × 5¹ × 11¹ × 113¹
LCM(660,678) = 74580