What is the Least Common Multiple of 45200 and 45214?

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 45200 and 45214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45200 and 45214, than apply into the LCM equation.

GCF(45200,45214) = 2
LCM(45200,45214) = ( 45200 × 45214) / 2
LCM(45200,45214) = 2043672800 / 2
LCM(45200,45214) = 1021836400

Least Common Multiple (LCM) of 45200 and 45214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45200 and 45214. First we will calculate the prime factors of 45200 and 45214.

Prime Factorization of 45200

Prime Factorization of 45214

Now multiplying the highest exponent prime factors to calculate the LCM of 45200 and 45214.

LCM(45200,45214) = 2⁴ × 5² × 113¹ × 13¹ × 37¹ × 47¹
LCM(45200,45214) = 1021836400