What is the Least Common Multiple of 75564 and 75584?

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 75564 and 75584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75564 and 75584, than apply into the LCM equation.

GCF(75564,75584) = 4
LCM(75564,75584) = ( 75564 × 75584) / 4
LCM(75564,75584) = 5711429376 / 4
LCM(75564,75584) = 1427857344

Least Common Multiple (LCM) of 75564 and 75584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75564 and 75584. First we will calculate the prime factors of 75564 and 75584.

Prime Factorization of 75564

Prime Factorization of 75584

Now multiplying the highest exponent prime factors to calculate the LCM of 75564 and 75584.

LCM(75564,75584) = 2⁶ × 3² × 2099¹ × 1181¹
LCM(75564,75584) = 1427857344