What is the Least Common Multiple of 8300 and 8312?

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 8300 and 8312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8300 and 8312, than apply into the LCM equation.

GCF(8300,8312) = 4
LCM(8300,8312) = ( 8300 × 8312) / 4
LCM(8300,8312) = 68989600 / 4
LCM(8300,8312) = 17247400

Least Common Multiple (LCM) of 8300 and 8312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8300 and 8312. First we will calculate the prime factors of 8300 and 8312.

Prime Factorization of 8300

Prime Factorization of 8312

Now multiplying the highest exponent prime factors to calculate the LCM of 8300 and 8312.

LCM(8300,8312) = 2³ × 5² × 83¹ × 1039¹
LCM(8300,8312) = 17247400