What is the Least Common Multiple of 45088 and 45100?

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 45088 and 45100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45088 and 45100, than apply into the LCM equation.

GCF(45088,45100) = 4
LCM(45088,45100) = ( 45088 × 45100) / 4
LCM(45088,45100) = 2033468800 / 4
LCM(45088,45100) = 508367200

Least Common Multiple (LCM) of 45088 and 45100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45088 and 45100. First we will calculate the prime factors of 45088 and 45100.

Prime Factorization of 45088

Prime Factorization of 45100

Now multiplying the highest exponent prime factors to calculate the LCM of 45088 and 45100.

LCM(45088,45100) = 2⁵ × 1409¹ × 5² × 11¹ × 41¹
LCM(45088,45100) = 508367200