What is the Least Common Multiple of 19576 and 19584?

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 19576 and 19584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19576 and 19584, than apply into the LCM equation.

GCF(19576,19584) = 8
LCM(19576,19584) = ( 19576 × 19584) / 8
LCM(19576,19584) = 383376384 / 8
LCM(19576,19584) = 47922048

Least Common Multiple (LCM) of 19576 and 19584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19576 and 19584. First we will calculate the prime factors of 19576 and 19584.

Prime Factorization of 19576

Prime Factorization of 19584

Now multiplying the highest exponent prime factors to calculate the LCM of 19576 and 19584.

LCM(19576,19584) = 2⁷ × 2447¹ × 3² × 17¹
LCM(19576,19584) = 47922048