What is the Least Common Multiple of 45114 and 45128?

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 45114 and 45128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45114 and 45128, than apply into the LCM equation.

GCF(45114,45128) = 2
LCM(45114,45128) = ( 45114 × 45128) / 2
LCM(45114,45128) = 2035904592 / 2
LCM(45114,45128) = 1017952296

Least Common Multiple (LCM) of 45114 and 45128 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45114 and 45128. First we will calculate the prime factors of 45114 and 45128.

Prime Factorization of 45114

Prime Factorization of 45128

Now multiplying the highest exponent prime factors to calculate the LCM of 45114 and 45128.

LCM(45114,45128) = 2³ × 3¹ × 73¹ × 103¹ × 5641¹
LCM(45114,45128) = 1017952296