What is the Least Common Multiple of 13600 and 13617?

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 13600 and 13617 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13600 and 13617, than apply into the LCM equation.

GCF(13600,13617) = 17
LCM(13600,13617) = ( 13600 × 13617) / 17
LCM(13600,13617) = 185191200 / 17
LCM(13600,13617) = 10893600

Least Common Multiple (LCM) of 13600 and 13617 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13600 and 13617. First we will calculate the prime factors of 13600 and 13617.

Prime Factorization of 13600

Prime Factorization of 13617

Now multiplying the highest exponent prime factors to calculate the LCM of 13600 and 13617.

LCM(13600,13617) = 2⁵ × 5² × 17¹ × 3² × 89¹
LCM(13600,13617) = 10893600