What is the Least Common Multiple of 1256 and 1275?

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 1256 and 1275 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1256 and 1275, than apply into the LCM equation.

GCF(1256,1275) = 1
LCM(1256,1275) = ( 1256 × 1275) / 1
LCM(1256,1275) = 1601400 / 1
LCM(1256,1275) = 1601400

Least Common Multiple (LCM) of 1256 and 1275 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1256 and 1275. First we will calculate the prime factors of 1256 and 1275.

Prime Factorization of 1256

Prime Factorization of 1275

Now multiplying the highest exponent prime factors to calculate the LCM of 1256 and 1275.

LCM(1256,1275) = 2³ × 157¹ × 3¹ × 5² × 17¹
LCM(1256,1275) = 1601400