What is the Least Common Multiple of 27564 and 27584?

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 27564 and 27584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27564 and 27584, than apply into the LCM equation.

GCF(27564,27584) = 4
LCM(27564,27584) = ( 27564 × 27584) / 4
LCM(27564,27584) = 760325376 / 4
LCM(27564,27584) = 190081344

Least Common Multiple (LCM) of 27564 and 27584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27564 and 27584. First we will calculate the prime factors of 27564 and 27584.

Prime Factorization of 27564

Prime Factorization of 27584

Now multiplying the highest exponent prime factors to calculate the LCM of 27564 and 27584.

LCM(27564,27584) = 2⁶ × 3¹ × 2297¹ × 431¹
LCM(27564,27584) = 190081344