What is the Least Common Multiple of 25824 and 25830?

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 25824 and 25830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25824 and 25830, than apply into the LCM equation.

GCF(25824,25830) = 6
LCM(25824,25830) = ( 25824 × 25830) / 6
LCM(25824,25830) = 667033920 / 6
LCM(25824,25830) = 111172320

Least Common Multiple (LCM) of 25824 and 25830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25824 and 25830. First we will calculate the prime factors of 25824 and 25830.

Prime Factorization of 25824

Prime Factorization of 25830

Now multiplying the highest exponent prime factors to calculate the LCM of 25824 and 25830.

LCM(25824,25830) = 2⁵ × 3² × 269¹ × 5¹ × 7¹ × 41¹
LCM(25824,25830) = 111172320