What is the Least Common Multiple of 23200 and 23214?

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 23200 and 23214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23200 and 23214, than apply into the LCM equation.

GCF(23200,23214) = 2
LCM(23200,23214) = ( 23200 × 23214) / 2
LCM(23200,23214) = 538564800 / 2
LCM(23200,23214) = 269282400

Least Common Multiple (LCM) of 23200 and 23214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23200 and 23214. First we will calculate the prime factors of 23200 and 23214.

Prime Factorization of 23200

Prime Factorization of 23214

Now multiplying the highest exponent prime factors to calculate the LCM of 23200 and 23214.

LCM(23200,23214) = 2⁵ × 5² × 29¹ × 3¹ × 53¹ × 73¹
LCM(23200,23214) = 269282400