What is the Least Common Multiple of 21600 and 21604?

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 21600 and 21604 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21600 and 21604, than apply into the LCM equation.

GCF(21600,21604) = 4
LCM(21600,21604) = ( 21600 × 21604) / 4
LCM(21600,21604) = 466646400 / 4
LCM(21600,21604) = 116661600

Least Common Multiple (LCM) of 21600 and 21604 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21600 and 21604. First we will calculate the prime factors of 21600 and 21604.

Prime Factorization of 21600

Prime Factorization of 21604

Now multiplying the highest exponent prime factors to calculate the LCM of 21600 and 21604.

LCM(21600,21604) = 2⁵ × 3³ × 5² × 11¹ × 491¹
LCM(21600,21604) = 116661600