What is the Least Common Multiple of 36300 and 36312?

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 36300 and 36312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36300 and 36312, than apply into the LCM equation.

GCF(36300,36312) = 12
LCM(36300,36312) = ( 36300 × 36312) / 12
LCM(36300,36312) = 1318125600 / 12
LCM(36300,36312) = 109843800

Least Common Multiple (LCM) of 36300 and 36312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36300 and 36312. First we will calculate the prime factors of 36300 and 36312.

Prime Factorization of 36300

Prime Factorization of 36312

Now multiplying the highest exponent prime factors to calculate the LCM of 36300 and 36312.

LCM(36300,36312) = 2³ × 3¹ × 5² × 11² × 17¹ × 89¹
LCM(36300,36312) = 109843800