What is the Least Common Multiple of 34800 and 34816?

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 34800 and 34816 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34800 and 34816, than apply into the LCM equation.

GCF(34800,34816) = 16
LCM(34800,34816) = ( 34800 × 34816) / 16
LCM(34800,34816) = 1211596800 / 16
LCM(34800,34816) = 75724800

Least Common Multiple (LCM) of 34800 and 34816 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34800 and 34816. First we will calculate the prime factors of 34800 and 34816.

Prime Factorization of 34800

Prime Factorization of 34816

Now multiplying the highest exponent prime factors to calculate the LCM of 34800 and 34816.

LCM(34800,34816) = 2¹¹ × 3¹ × 5² × 29¹ × 17¹
LCM(34800,34816) = 75724800