What is the Least Common Multiple of 45000 and 45008?

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 45000 and 45008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45000 and 45008, than apply into the LCM equation.

GCF(45000,45008) = 8
LCM(45000,45008) = ( 45000 × 45008) / 8
LCM(45000,45008) = 2025360000 / 8
LCM(45000,45008) = 253170000

Least Common Multiple (LCM) of 45000 and 45008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45000 and 45008. First we will calculate the prime factors of 45000 and 45008.

Prime Factorization of 45000

Prime Factorization of 45008

Now multiplying the highest exponent prime factors to calculate the LCM of 45000 and 45008.

LCM(45000,45008) = 2⁴ × 3² × 5⁴ × 29¹ × 97¹
LCM(45000,45008) = 253170000