What is the Least Common Multiple of 39500 and 39520?

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 39500 and 39520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39500 and 39520, than apply into the LCM equation.

GCF(39500,39520) = 20
LCM(39500,39520) = ( 39500 × 39520) / 20
LCM(39500,39520) = 1561040000 / 20
LCM(39500,39520) = 78052000

Least Common Multiple (LCM) of 39500 and 39520 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39500 and 39520. First we will calculate the prime factors of 39500 and 39520.

Prime Factorization of 39500

Prime Factorization of 39520

Now multiplying the highest exponent prime factors to calculate the LCM of 39500 and 39520.

LCM(39500,39520) = 2⁵ × 5³ × 79¹ × 13¹ × 19¹
LCM(39500,39520) = 78052000