What is the Least Common Multiple of 654 and 669?

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 669 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 669, than apply into the LCM equation.

GCF(654,669) = 3
LCM(654,669) = ( 654 × 669) / 3
LCM(654,669) = 437526 / 3
LCM(654,669) = 145842

Least Common Multiple (LCM) of 654 and 669 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 654 and 669. First we will calculate the prime factors of 654 and 669.

Prime Factorization of 654

Prime Factorization of 669

Now multiplying the highest exponent prime factors to calculate the LCM of 654 and 669.

LCM(654,669) = 2¹ × 3¹ × 109¹ × 223¹
LCM(654,669) = 145842