What is the Least Common Multiple of 90300 and 90315?

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 90300 and 90315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90300 and 90315, than apply into the LCM equation.

GCF(90300,90315) = 15
LCM(90300,90315) = ( 90300 × 90315) / 15
LCM(90300,90315) = 8155444500 / 15
LCM(90300,90315) = 543696300

Least Common Multiple (LCM) of 90300 and 90315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90300 and 90315. First we will calculate the prime factors of 90300 and 90315.

Prime Factorization of 90300

Prime Factorization of 90315

Now multiplying the highest exponent prime factors to calculate the LCM of 90300 and 90315.

LCM(90300,90315) = 2² × 3⁴ × 5² × 7¹ × 43¹ × 223¹
LCM(90300,90315) = 543696300