What is the Least Common Multiple of 1300 and 1314?

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 1314 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 1314, than apply into the LCM equation.

GCF(1300,1314) = 2
LCM(1300,1314) = ( 1300 × 1314) / 2
LCM(1300,1314) = 1708200 / 2
LCM(1300,1314) = 854100

Least Common Multiple (LCM) of 1300 and 1314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1300 and 1314. First we will calculate the prime factors of 1300 and 1314.

Prime Factorization of 1300

Prime Factorization of 1314

Now multiplying the highest exponent prime factors to calculate the LCM of 1300 and 1314.

LCM(1300,1314) = 2² × 5² × 13¹ × 3² × 73¹
LCM(1300,1314) = 854100