What is the Least Common Multiple of 654 and 660?

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 654 and 660 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 654 and 660, than apply into the LCM equation.

GCF(654,660) = 6
LCM(654,660) = ( 654 × 660) / 6
LCM(654,660) = 431640 / 6
LCM(654,660) = 71940

Least Common Multiple (LCM) of 654 and 660 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 654 and 660. First we will calculate the prime factors of 654 and 660.

Prime Factorization of 654

Prime Factorization of 660

Now multiplying the highest exponent prime factors to calculate the LCM of 654 and 660.

LCM(654,660) = 2² × 3¹ × 109¹ × 5¹ × 11¹
LCM(654,660) = 71940