What is the Least Common Multiple of 17712 and 17732?

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 17712 and 17732 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17712 and 17732, than apply into the LCM equation.

GCF(17712,17732) = 4
LCM(17712,17732) = ( 17712 × 17732) / 4
LCM(17712,17732) = 314069184 / 4
LCM(17712,17732) = 78517296

Least Common Multiple (LCM) of 17712 and 17732 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17712 and 17732. First we will calculate the prime factors of 17712 and 17732.

Prime Factorization of 17712

Prime Factorization of 17732

Now multiplying the highest exponent prime factors to calculate the LCM of 17712 and 17732.

LCM(17712,17732) = 2⁴ × 3³ × 41¹ × 11¹ × 13¹ × 31¹
LCM(17712,17732) = 78517296