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What is the Least Common Multiple of 12816 and 12834?

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 12816 and 12834 is 9137808.

LCM(12816,12834) = 9137808

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Least Common Multiple of 12816 and 12834 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12816 and 12834, than apply into the LCM equation.

GCF(12816,12834) = 18
LCM(12816,12834) = ( 12816 × 12834) / 18
LCM(12816,12834) = 164480544 / 18
LCM(12816,12834) = 9137808

Least Common Multiple (LCM) of 12816 and 12834 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12816 and 12834. First we will calculate the prime factors of 12816 and 12834.

Prime Factorization of 12816

Prime factors of 12816 are 2, 3, 89. Prime factorization of 12816 in exponential form is:

12816 = 24 × 32 × 891

Prime Factorization of 12834

Prime factors of 12834 are 2, 3, 23, 31. Prime factorization of 12834 in exponential form is:

12834 = 21 × 32 × 231 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 12816 and 12834.

LCM(12816,12834) = 24 × 32 × 891 × 231 × 311
LCM(12816,12834) = 9137808