What is the Least Common Multiple of 7564 and 7584?

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 7564 and 7584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7564 and 7584, than apply into the LCM equation.

GCF(7564,7584) = 4
LCM(7564,7584) = ( 7564 × 7584) / 4
LCM(7564,7584) = 57365376 / 4
LCM(7564,7584) = 14341344

Least Common Multiple (LCM) of 7564 and 7584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7564 and 7584. First we will calculate the prime factors of 7564 and 7584.

Prime Factorization of 7564

Prime Factorization of 7584

Now multiplying the highest exponent prime factors to calculate the LCM of 7564 and 7584.

LCM(7564,7584) = 2⁵ × 31¹ × 61¹ × 3¹ × 79¹
LCM(7564,7584) = 14341344