What is the Least Common Multiple of 7500 and 7519?

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 7500 and 7519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7500 and 7519, than apply into the LCM equation.

GCF(7500,7519) = 1
LCM(7500,7519) = ( 7500 × 7519) / 1
LCM(7500,7519) = 56392500 / 1
LCM(7500,7519) = 56392500

Least Common Multiple (LCM) of 7500 and 7519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7500 and 7519. First we will calculate the prime factors of 7500 and 7519.

Prime Factorization of 7500

Prime Factorization of 7519

Now multiplying the highest exponent prime factors to calculate the LCM of 7500 and 7519.

LCM(7500,7519) = 2² × 3¹ × 5⁴ × 73¹ × 103¹
LCM(7500,7519) = 56392500