What is the Least Common Multiple of 45090 and 45105?

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 45090 and 45105 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45090 and 45105, than apply into the LCM equation.

GCF(45090,45105) = 15
LCM(45090,45105) = ( 45090 × 45105) / 15
LCM(45090,45105) = 2033784450 / 15
LCM(45090,45105) = 135585630

Least Common Multiple (LCM) of 45090 and 45105 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45090 and 45105. First we will calculate the prime factors of 45090 and 45105.

Prime Factorization of 45090

Prime Factorization of 45105

Now multiplying the highest exponent prime factors to calculate the LCM of 45090 and 45105.

LCM(45090,45105) = 2¹ × 3³ × 5¹ × 167¹ × 31¹ × 97¹
LCM(45090,45105) = 135585630