What is the Least Common Multiple of 642 and 657?

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 642 and 657 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 642 and 657, than apply into the LCM equation.

GCF(642,657) = 3
LCM(642,657) = ( 642 × 657) / 3
LCM(642,657) = 421794 / 3
LCM(642,657) = 140598

Least Common Multiple (LCM) of 642 and 657 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 642 and 657. First we will calculate the prime factors of 642 and 657.

Prime Factorization of 642

Prime Factorization of 657

Now multiplying the highest exponent prime factors to calculate the LCM of 642 and 657.

LCM(642,657) = 2¹ × 3² × 107¹ × 73¹
LCM(642,657) = 140598