What is the Least Common Multiple of 45714 and 45728?

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 45714 and 45728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45714 and 45728, than apply into the LCM equation.

GCF(45714,45728) = 2
LCM(45714,45728) = ( 45714 × 45728) / 2
LCM(45714,45728) = 2090409792 / 2
LCM(45714,45728) = 1045204896

Least Common Multiple (LCM) of 45714 and 45728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45714 and 45728. First we will calculate the prime factors of 45714 and 45728.

Prime Factorization of 45714

Prime Factorization of 45728

Now multiplying the highest exponent prime factors to calculate the LCM of 45714 and 45728.

LCM(45714,45728) = 2⁵ × 3¹ × 19¹ × 401¹ × 1429¹
LCM(45714,45728) = 1045204896