What is the Least Common Multiple of 65200 and 65214?

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 65200 and 65214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65200 and 65214, than apply into the LCM equation.

GCF(65200,65214) = 2
LCM(65200,65214) = ( 65200 × 65214) / 2
LCM(65200,65214) = 4251952800 / 2
LCM(65200,65214) = 2125976400

Least Common Multiple (LCM) of 65200 and 65214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65200 and 65214. First we will calculate the prime factors of 65200 and 65214.

Prime Factorization of 65200

Prime Factorization of 65214

Now multiplying the highest exponent prime factors to calculate the LCM of 65200 and 65214.

LCM(65200,65214) = 2⁴ × 5² × 163¹ × 3² × 3623¹
LCM(65200,65214) = 2125976400