What is the Least Common Multiple of 17712 and 17724?

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 17724 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 17724, than apply into the LCM equation.

GCF(17712,17724) = 12
LCM(17712,17724) = ( 17712 × 17724) / 12
LCM(17712,17724) = 313927488 / 12
LCM(17712,17724) = 26160624

Least Common Multiple (LCM) of 17712 and 17724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17712 and 17724. First we will calculate the prime factors of 17712 and 17724.

Prime Factorization of 17712

Prime Factorization of 17724

Now multiplying the highest exponent prime factors to calculate the LCM of 17712 and 17724.

LCM(17712,17724) = 2⁴ × 3³ × 41¹ × 7¹ × 211¹
LCM(17712,17724) = 26160624