What is the Least Common Multiple of 45105 and 45112?

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 45112 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 45112, than apply into the LCM equation.

GCF(45105,45112) = 1
LCM(45105,45112) = ( 45105 × 45112) / 1
LCM(45105,45112) = 2034776760 / 1
LCM(45105,45112) = 2034776760

Least Common Multiple (LCM) of 45105 and 45112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45105 and 45112. First we will calculate the prime factors of 45105 and 45112.

Prime Factorization of 45105

Prime Factorization of 45112

Now multiplying the highest exponent prime factors to calculate the LCM of 45105 and 45112.

LCM(45105,45112) = 3¹ × 5¹ × 31¹ × 97¹ × 2³ × 5639¹
LCM(45105,45112) = 2034776760