What is the Least Common Multiple of 39480 and 39500?

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 39480 and 39500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39480 and 39500, than apply into the LCM equation.

GCF(39480,39500) = 20
LCM(39480,39500) = ( 39480 × 39500) / 20
LCM(39480,39500) = 1559460000 / 20
LCM(39480,39500) = 77973000

Least Common Multiple (LCM) of 39480 and 39500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39480 and 39500. First we will calculate the prime factors of 39480 and 39500.

Prime Factorization of 39480

Prime Factorization of 39500

Now multiplying the highest exponent prime factors to calculate the LCM of 39480 and 39500.

LCM(39480,39500) = 2³ × 3¹ × 5³ × 7¹ × 47¹ × 79¹
LCM(39480,39500) = 77973000