What is the Least Common Multiple of 99300 and 99312?

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 99300 and 99312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99300 and 99312, than apply into the LCM equation.

GCF(99300,99312) = 12
LCM(99300,99312) = ( 99300 × 99312) / 12
LCM(99300,99312) = 9861681600 / 12
LCM(99300,99312) = 821806800

Least Common Multiple (LCM) of 99300 and 99312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 99300 and 99312. First we will calculate the prime factors of 99300 and 99312.

Prime Factorization of 99300

Prime Factorization of 99312

Now multiplying the highest exponent prime factors to calculate the LCM of 99300 and 99312.

LCM(99300,99312) = 2⁴ × 3¹ × 5² × 331¹ × 2069¹
LCM(99300,99312) = 821806800