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What is the Least Common Multiple of 10800 and 10814?

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 10800 and 10814 is 58395600.

LCM(10800,10814) = 58395600

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Least Common Multiple of 10800 and 10814 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10800 and 10814, than apply into the LCM equation.

GCF(10800,10814) = 2
LCM(10800,10814) = ( 10800 × 10814) / 2
LCM(10800,10814) = 116791200 / 2
LCM(10800,10814) = 58395600

Least Common Multiple (LCM) of 10800 and 10814 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10800 and 10814. First we will calculate the prime factors of 10800 and 10814.

Prime Factorization of 10800

Prime factors of 10800 are 2, 3, 5. Prime factorization of 10800 in exponential form is:

10800 = 24 × 33 × 52

Prime Factorization of 10814

Prime factors of 10814 are 2, 5407. Prime factorization of 10814 in exponential form is:

10814 = 21 × 54071

Now multiplying the highest exponent prime factors to calculate the LCM of 10800 and 10814.

LCM(10800,10814) = 24 × 33 × 52 × 54071
LCM(10800,10814) = 58395600