What is the Least Common Multiple of 90000 and 90015?

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 90000 and 90015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90000 and 90015, than apply into the LCM equation.

GCF(90000,90015) = 15
LCM(90000,90015) = ( 90000 × 90015) / 15
LCM(90000,90015) = 8101350000 / 15
LCM(90000,90015) = 540090000

Least Common Multiple (LCM) of 90000 and 90015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90000 and 90015. First we will calculate the prime factors of 90000 and 90015.

Prime Factorization of 90000

Prime Factorization of 90015

Now multiplying the highest exponent prime factors to calculate the LCM of 90000 and 90015.

LCM(90000,90015) = 2⁴ × 3² × 5⁴ × 17¹ × 353¹
LCM(90000,90015) = 540090000