What is the Least Common Multiple of 75840 and 75854?

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 75854 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 75854, than apply into the LCM equation.

GCF(75840,75854) = 2
LCM(75840,75854) = ( 75840 × 75854) / 2
LCM(75840,75854) = 5752767360 / 2
LCM(75840,75854) = 2876383680

Least Common Multiple (LCM) of 75840 and 75854 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75840 and 75854. First we will calculate the prime factors of 75840 and 75854.

Prime Factorization of 75840

Prime Factorization of 75854

Now multiplying the highest exponent prime factors to calculate the LCM of 75840 and 75854.

LCM(75840,75854) = 2⁶ × 3¹ × 5¹ × 79¹ × 17¹ × 23¹ × 97¹
LCM(75840,75854) = 2876383680