What is the Least Common Multiple of 45105 and 45117?

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 45105 and 45117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45105 and 45117, than apply into the LCM equation.

GCF(45105,45117) = 3
LCM(45105,45117) = ( 45105 × 45117) / 3
LCM(45105,45117) = 2035002285 / 3
LCM(45105,45117) = 678334095

Least Common Multiple (LCM) of 45105 and 45117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45105 and 45117. First we will calculate the prime factors of 45105 and 45117.

Prime Factorization of 45105

Prime Factorization of 45117

Now multiplying the highest exponent prime factors to calculate the LCM of 45105 and 45117.

LCM(45105,45117) = 3⁴ × 5¹ × 31¹ × 97¹ × 557¹
LCM(45105,45117) = 678334095