What is the Least Common Multiple of 59808 and 59823?

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 59808 and 59823 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 59808 and 59823, than apply into the LCM equation.

GCF(59808,59823) = 3
LCM(59808,59823) = ( 59808 × 59823) / 3
LCM(59808,59823) = 3577893984 / 3
LCM(59808,59823) = 1192631328

Least Common Multiple (LCM) of 59808 and 59823 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 59808 and 59823. First we will calculate the prime factors of 59808 and 59823.

Prime Factorization of 59808

Prime Factorization of 59823

Now multiplying the highest exponent prime factors to calculate the LCM of 59808 and 59823.

LCM(59808,59823) = 2⁵ × 3² × 7¹ × 89¹ × 17² × 23¹
LCM(59808,59823) = 1192631328