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What is the Least Common Multiple of 1856 and 1872?

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 1856 and 1872 is 217152.

LCM(1856,1872) = 217152

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Least Common Multiple of 1856 and 1872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1856 and 1872, than apply into the LCM equation.

GCF(1856,1872) = 16
LCM(1856,1872) = ( 1856 × 1872) / 16
LCM(1856,1872) = 3474432 / 16
LCM(1856,1872) = 217152

Least Common Multiple (LCM) of 1856 and 1872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1856 and 1872. First we will calculate the prime factors of 1856 and 1872.

Prime Factorization of 1856

Prime factors of 1856 are 2, 29. Prime factorization of 1856 in exponential form is:

1856 = 26 × 291

Prime Factorization of 1872

Prime factors of 1872 are 2, 3, 13. Prime factorization of 1872 in exponential form is:

1872 = 24 × 32 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 1856 and 1872.

LCM(1856,1872) = 26 × 291 × 32 × 131
LCM(1856,1872) = 217152