What is the Least Common Multiple of 75828 and 75840?

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 75828 and 75840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75828 and 75840, than apply into the LCM equation.

GCF(75828,75840) = 12
LCM(75828,75840) = ( 75828 × 75840) / 12
LCM(75828,75840) = 5750795520 / 12
LCM(75828,75840) = 479232960

Least Common Multiple (LCM) of 75828 and 75840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75828 and 75840. First we will calculate the prime factors of 75828 and 75840.

Prime Factorization of 75828

Prime Factorization of 75840

Now multiplying the highest exponent prime factors to calculate the LCM of 75828 and 75840.

LCM(75828,75840) = 2⁶ × 3¹ × 71¹ × 89¹ × 5¹ × 79¹
LCM(75828,75840) = 479232960