What is the Least Common Multiple of 31300 and 31312?

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 31300 and 31312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31300 and 31312, than apply into the LCM equation.

GCF(31300,31312) = 4
LCM(31300,31312) = ( 31300 × 31312) / 4
LCM(31300,31312) = 980065600 / 4
LCM(31300,31312) = 245016400

Least Common Multiple (LCM) of 31300 and 31312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31300 and 31312. First we will calculate the prime factors of 31300 and 31312.

Prime Factorization of 31300

Prime Factorization of 31312

Now multiplying the highest exponent prime factors to calculate the LCM of 31300 and 31312.

LCM(31300,31312) = 2⁴ × 5² × 313¹ × 19¹ × 103¹
LCM(31300,31312) = 245016400