What is the Least Common Multiple of 2500 and 2514?

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 2500 and 2514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2500 and 2514, than apply into the LCM equation.

GCF(2500,2514) = 2
LCM(2500,2514) = ( 2500 × 2514) / 2
LCM(2500,2514) = 6285000 / 2
LCM(2500,2514) = 3142500

Least Common Multiple (LCM) of 2500 and 2514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2500 and 2514. First we will calculate the prime factors of 2500 and 2514.

Prime Factorization of 2500

Prime Factorization of 2514

Now multiplying the highest exponent prime factors to calculate the LCM of 2500 and 2514.

LCM(2500,2514) = 2² × 5⁴ × 3¹ × 419¹
LCM(2500,2514) = 3142500