What is the Least Common Multiple of 638 and 648?

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 638 and 648 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 638 and 648, than apply into the LCM equation.

GCF(638,648) = 2
LCM(638,648) = ( 638 × 648) / 2
LCM(638,648) = 413424 / 2
LCM(638,648) = 206712

Least Common Multiple (LCM) of 638 and 648 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 638 and 648. First we will calculate the prime factors of 638 and 648.

Prime Factorization of 638

Prime Factorization of 648

Now multiplying the highest exponent prime factors to calculate the LCM of 638 and 648.

LCM(638,648) = 2³ × 11¹ × 29¹ × 3⁴
LCM(638,648) = 206712