What is the Least Common Multiple of 90105 and 90120?

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 90105 and 90120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90105 and 90120, than apply into the LCM equation.

GCF(90105,90120) = 15
LCM(90105,90120) = ( 90105 × 90120) / 15
LCM(90105,90120) = 8120262600 / 15
LCM(90105,90120) = 541350840

Least Common Multiple (LCM) of 90105 and 90120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 90105 and 90120. First we will calculate the prime factors of 90105 and 90120.

Prime Factorization of 90105

Prime Factorization of 90120

Now multiplying the highest exponent prime factors to calculate the LCM of 90105 and 90120.

LCM(90105,90120) = 3¹ × 5¹ × 6007¹ × 2³ × 751¹
LCM(90105,90120) = 541350840