What is the Least Common Multiple of 5000 and 5008?

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 5008 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 5008, than apply into the LCM equation.

GCF(5000,5008) = 8
LCM(5000,5008) = ( 5000 × 5008) / 8
LCM(5000,5008) = 25040000 / 8
LCM(5000,5008) = 3130000

Least Common Multiple (LCM) of 5000 and 5008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5000 and 5008. First we will calculate the prime factors of 5000 and 5008.

Prime Factorization of 5000

Prime Factorization of 5008

Now multiplying the highest exponent prime factors to calculate the LCM of 5000 and 5008.

LCM(5000,5008) = 2⁴ × 5⁴ × 313¹
LCM(5000,5008) = 3130000