What is the Least Common Multiple of 39675 and 39680?

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 39675 and 39680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39675 and 39680, than apply into the LCM equation.

GCF(39675,39680) = 5
LCM(39675,39680) = ( 39675 × 39680) / 5
LCM(39675,39680) = 1574304000 / 5
LCM(39675,39680) = 314860800

Least Common Multiple (LCM) of 39675 and 39680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39675 and 39680. First we will calculate the prime factors of 39675 and 39680.

Prime Factorization of 39675

Prime Factorization of 39680

Now multiplying the highest exponent prime factors to calculate the LCM of 39675 and 39680.

LCM(39675,39680) = 3¹ × 5² × 23² × 2⁸ × 31¹
LCM(39675,39680) = 314860800