What is the Least Common Multiple of 73584 and 73600?

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 73584 and 73600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 73584 and 73600, than apply into the LCM equation.

GCF(73584,73600) = 16
LCM(73584,73600) = ( 73584 × 73600) / 16
LCM(73584,73600) = 5415782400 / 16
LCM(73584,73600) = 338486400

Least Common Multiple (LCM) of 73584 and 73600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 73584 and 73600. First we will calculate the prime factors of 73584 and 73600.

Prime Factorization of 73584

Prime Factorization of 73600

Now multiplying the highest exponent prime factors to calculate the LCM of 73584 and 73600.

LCM(73584,73600) = 2⁷ × 3² × 7¹ × 73¹ × 5² × 23¹
LCM(73584,73600) = 338486400