What is the Least Common Multiple of 45100 and 45120?

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 45100 and 45120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45100 and 45120, than apply into the LCM equation.

GCF(45100,45120) = 20
LCM(45100,45120) = ( 45100 × 45120) / 20
LCM(45100,45120) = 2034912000 / 20
LCM(45100,45120) = 101745600

Least Common Multiple (LCM) of 45100 and 45120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45100 and 45120. First we will calculate the prime factors of 45100 and 45120.

Prime Factorization of 45100

Prime Factorization of 45120

Now multiplying the highest exponent prime factors to calculate the LCM of 45100 and 45120.

LCM(45100,45120) = 2⁶ × 5² × 11¹ × 41¹ × 3¹ × 47¹
LCM(45100,45120) = 101745600