What is the Least Common Multiple of 2250 and 2256?

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 2250 and 2256 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2250 and 2256, than apply into the LCM equation.

GCF(2250,2256) = 6
LCM(2250,2256) = ( 2250 × 2256) / 6
LCM(2250,2256) = 5076000 / 6
LCM(2250,2256) = 846000

Least Common Multiple (LCM) of 2250 and 2256 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2250 and 2256. First we will calculate the prime factors of 2250 and 2256.

Prime Factorization of 2250

Prime Factorization of 2256

Now multiplying the highest exponent prime factors to calculate the LCM of 2250 and 2256.

LCM(2250,2256) = 2⁴ × 3² × 5³ × 47¹
LCM(2250,2256) = 846000