What is the Least Common Multiple of 45306 and 45312?

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 45306 and 45312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45306 and 45312, than apply into the LCM equation.

GCF(45306,45312) = 6
LCM(45306,45312) = ( 45306 × 45312) / 6
LCM(45306,45312) = 2052905472 / 6
LCM(45306,45312) = 342150912

Least Common Multiple (LCM) of 45306 and 45312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45306 and 45312. First we will calculate the prime factors of 45306 and 45312.

Prime Factorization of 45306

Prime Factorization of 45312

Now multiplying the highest exponent prime factors to calculate the LCM of 45306 and 45312.

LCM(45306,45312) = 2⁸ × 3³ × 839¹ × 59¹
LCM(45306,45312) = 342150912