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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 (LCM) of 1256 and 1275 is 1601400.

LCM(1256,1275) = 1601400

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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 factors of 1256 are 2, 157. Prime factorization of 1256 in exponential form is:

1256 = 23 × 1571

Prime Factorization of 1275

Prime factors of 1275 are 3, 5, 17. Prime factorization of 1275 in exponential form is:

1275 = 31 × 52 × 171

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