What is the Least Common Multiple of 3675 and 3688?

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 3675 and 3688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3675 and 3688, than apply into the LCM equation.

GCF(3675,3688) = 1
LCM(3675,3688) = ( 3675 × 3688) / 1
LCM(3675,3688) = 13553400 / 1
LCM(3675,3688) = 13553400

Least Common Multiple (LCM) of 3675 and 3688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3675 and 3688. First we will calculate the prime factors of 3675 and 3688.

Prime Factorization of 3675

Prime Factorization of 3688

Now multiplying the highest exponent prime factors to calculate the LCM of 3675 and 3688.

LCM(3675,3688) = 3¹ × 5² × 7² × 2³ × 461¹
LCM(3675,3688) = 13553400