What is the Least Common Multiple of 38584 and 38592?

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 38584 and 38592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38584 and 38592, than apply into the LCM equation.

GCF(38584,38592) = 8
LCM(38584,38592) = ( 38584 × 38592) / 8
LCM(38584,38592) = 1489033728 / 8
LCM(38584,38592) = 186129216

Least Common Multiple (LCM) of 38584 and 38592 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38584 and 38592. First we will calculate the prime factors of 38584 and 38592.

Prime Factorization of 38584

Prime Factorization of 38592

Now multiplying the highest exponent prime factors to calculate the LCM of 38584 and 38592.

LCM(38584,38592) = 2⁶ × 7¹ × 13¹ × 53¹ × 3² × 67¹
LCM(38584,38592) = 186129216