What is the Least Common Multiple of 3675 and 3680?

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 3680 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 3680, than apply into the LCM equation.

GCF(3675,3680) = 5
LCM(3675,3680) = ( 3675 × 3680) / 5
LCM(3675,3680) = 13524000 / 5
LCM(3675,3680) = 2704800

Least Common Multiple (LCM) of 3675 and 3680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3675 and 3680. First we will calculate the prime factors of 3675 and 3680.

Prime Factorization of 3675

Prime Factorization of 3680

Now multiplying the highest exponent prime factors to calculate the LCM of 3675 and 3680.

LCM(3675,3680) = 3¹ × 5² × 7² × 2⁵ × 23¹
LCM(3675,3680) = 2704800