What is the Least Common Multiple of 90208 and 90214?

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 90208 and 90214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90208 and 90214, than apply into the LCM equation.

GCF(90208,90214) = 2
LCM(90208,90214) = ( 90208 × 90214) / 2
LCM(90208,90214) = 8138024512 / 2
LCM(90208,90214) = 4069012256

Least Common Multiple (LCM) of 90208 and 90214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90208 and 90214. First we will calculate the prime factors of 90208 and 90214.

Prime Factorization of 90208

Prime Factorization of 90214

Now multiplying the highest exponent prime factors to calculate the LCM of 90208 and 90214.

LCM(90208,90214) = 2⁵ × 2819¹ × 43¹ × 1049¹
LCM(90208,90214) = 4069012256