What is the Least Common Multiple of 22500 and 22519?

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 22500 and 22519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 22500 and 22519, than apply into the LCM equation.

GCF(22500,22519) = 1
LCM(22500,22519) = ( 22500 × 22519) / 1
LCM(22500,22519) = 506677500 / 1
LCM(22500,22519) = 506677500

Least Common Multiple (LCM) of 22500 and 22519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 22500 and 22519. First we will calculate the prime factors of 22500 and 22519.

Prime Factorization of 22500

Prime Factorization of 22519

Now multiplying the highest exponent prime factors to calculate the LCM of 22500 and 22519.

LCM(22500,22519) = 2² × 3² × 5⁴ × 7¹ × 3217¹
LCM(22500,22519) = 506677500