What is the Least Common Multiple of 1200 and 1214?

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 1200 and 1214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1200 and 1214, than apply into the LCM equation.

GCF(1200,1214) = 2
LCM(1200,1214) = ( 1200 × 1214) / 2
LCM(1200,1214) = 1456800 / 2
LCM(1200,1214) = 728400

Least Common Multiple (LCM) of 1200 and 1214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1200 and 1214. First we will calculate the prime factors of 1200 and 1214.

Prime Factorization of 1200

Prime Factorization of 1214

Now multiplying the highest exponent prime factors to calculate the LCM of 1200 and 1214.

LCM(1200,1214) = 2⁴ × 3¹ × 5² × 607¹
LCM(1200,1214) = 728400