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What is the Least Common Multiple of 2240 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 (LCM) of 2240 and 2256 is 315840.

LCM(2240,2256) = 315840

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Least Common Multiple of 2240 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 2240 and 2256, than apply into the LCM equation.

GCF(2240,2256) = 16
LCM(2240,2256) = ( 2240 × 2256) / 16
LCM(2240,2256) = 5053440 / 16
LCM(2240,2256) = 315840

Least Common Multiple (LCM) of 2240 and 2256 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2240 and 2256. First we will calculate the prime factors of 2240 and 2256.

Prime Factorization of 2240

Prime factors of 2240 are 2, 5, 7. Prime factorization of 2240 in exponential form is:

2240 = 26 × 51 × 71

Prime Factorization of 2256

Prime factors of 2256 are 2, 3, 47. Prime factorization of 2256 in exponential form is:

2256 = 24 × 31 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 2240 and 2256.

LCM(2240,2256) = 26 × 51 × 71 × 31 × 471
LCM(2240,2256) = 315840