What is the Least Common Multiple of 1300 and 1312?

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 1300 and 1312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1300 and 1312, than apply into the LCM equation.

GCF(1300,1312) = 4
LCM(1300,1312) = ( 1300 × 1312) / 4
LCM(1300,1312) = 1705600 / 4
LCM(1300,1312) = 426400

Least Common Multiple (LCM) of 1300 and 1312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1300 and 1312. First we will calculate the prime factors of 1300 and 1312.

Prime Factorization of 1300

Prime Factorization of 1312

Now multiplying the highest exponent prime factors to calculate the LCM of 1300 and 1312.

LCM(1300,1312) = 2⁵ × 5² × 13¹ × 41¹
LCM(1300,1312) = 426400