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What is the Least Common Multiple of 54800 and 54816?

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 54800 and 54816 is 187744800.

LCM(54800,54816) = 187744800

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Least Common Multiple of 54800 and 54816 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54800 and 54816, than apply into the LCM equation.

GCF(54800,54816) = 16
LCM(54800,54816) = ( 54800 × 54816) / 16
LCM(54800,54816) = 3003916800 / 16
LCM(54800,54816) = 187744800

Least Common Multiple (LCM) of 54800 and 54816 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54800 and 54816. First we will calculate the prime factors of 54800 and 54816.

Prime Factorization of 54800

Prime factors of 54800 are 2, 5, 137. Prime factorization of 54800 in exponential form is:

54800 = 24 × 52 × 1371

Prime Factorization of 54816

Prime factors of 54816 are 2, 3, 571. Prime factorization of 54816 in exponential form is:

54816 = 25 × 31 × 5711

Now multiplying the highest exponent prime factors to calculate the LCM of 54800 and 54816.

LCM(54800,54816) = 25 × 52 × 1371 × 31 × 5711
LCM(54800,54816) = 187744800