What is the Least Common Multiple of 5000 and 5010?

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 5000 and 5010 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5000 and 5010, than apply into the LCM equation.

GCF(5000,5010) = 10
LCM(5000,5010) = ( 5000 × 5010) / 10
LCM(5000,5010) = 25050000 / 10
LCM(5000,5010) = 2505000

Least Common Multiple (LCM) of 5000 and 5010 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5000 and 5010. First we will calculate the prime factors of 5000 and 5010.

Prime Factorization of 5000

Prime Factorization of 5010

Now multiplying the highest exponent prime factors to calculate the LCM of 5000 and 5010.

LCM(5000,5010) = 2³ × 5⁴ × 3¹ × 167¹
LCM(5000,5010) = 2505000