What is the Least Common Multiple of 90200 and 90208?

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 90200 and 90208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90200 and 90208, than apply into the LCM equation.

GCF(90200,90208) = 8
LCM(90200,90208) = ( 90200 × 90208) / 8
LCM(90200,90208) = 8136761600 / 8
LCM(90200,90208) = 1017095200

Least Common Multiple (LCM) of 90200 and 90208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90200 and 90208. First we will calculate the prime factors of 90200 and 90208.

Prime Factorization of 90200

Prime Factorization of 90208

Now multiplying the highest exponent prime factors to calculate the LCM of 90200 and 90208.

LCM(90200,90208) = 2⁵ × 5² × 11¹ × 41¹ × 2819¹
LCM(90200,90208) = 1017095200