What is the Least Common Multiple of 2256 and 2275?

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 2256 and 2275 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2256 and 2275, than apply into the LCM equation.

GCF(2256,2275) = 1
LCM(2256,2275) = ( 2256 × 2275) / 1
LCM(2256,2275) = 5132400 / 1
LCM(2256,2275) = 5132400

Least Common Multiple (LCM) of 2256 and 2275 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2256 and 2275. First we will calculate the prime factors of 2256 and 2275.

Prime Factorization of 2256

Prime Factorization of 2275

Now multiplying the highest exponent prime factors to calculate the LCM of 2256 and 2275.

LCM(2256,2275) = 2⁴ × 3¹ × 47¹ × 5² × 7¹ × 13¹
LCM(2256,2275) = 5132400