What is the Least Common Multiple of 75840 and 75860?

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 75840 and 75860 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75840 and 75860, than apply into the LCM equation.

GCF(75840,75860) = 20
LCM(75840,75860) = ( 75840 × 75860) / 20
LCM(75840,75860) = 5753222400 / 20
LCM(75840,75860) = 287661120

Least Common Multiple (LCM) of 75840 and 75860 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75840 and 75860. First we will calculate the prime factors of 75840 and 75860.

Prime Factorization of 75840

Prime Factorization of 75860

Now multiplying the highest exponent prime factors to calculate the LCM of 75840 and 75860.

LCM(75840,75860) = 2⁶ × 3¹ × 5¹ × 79¹ × 3793¹
LCM(75840,75860) = 287661120