What is the Least Common Multiple of 23564 and 23584?

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 23564 and 23584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23564 and 23584, than apply into the LCM equation.

GCF(23564,23584) = 4
LCM(23564,23584) = ( 23564 × 23584) / 4
LCM(23564,23584) = 555733376 / 4
LCM(23564,23584) = 138933344

Least Common Multiple (LCM) of 23564 and 23584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23564 and 23584. First we will calculate the prime factors of 23564 and 23584.

Prime Factorization of 23564

Prime Factorization of 23584

Now multiplying the highest exponent prime factors to calculate the LCM of 23564 and 23584.

LCM(23564,23584) = 2⁵ × 43¹ × 137¹ × 11¹ × 67¹
LCM(23564,23584) = 138933344