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What is the Least Common Multiple of 10806 and 10824?

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 10806 and 10824 is 19494024.

LCM(10806,10824) = 19494024

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Least Common Multiple of 10806 and 10824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10806 and 10824, than apply into the LCM equation.

GCF(10806,10824) = 6
LCM(10806,10824) = ( 10806 × 10824) / 6
LCM(10806,10824) = 116964144 / 6
LCM(10806,10824) = 19494024

Least Common Multiple (LCM) of 10806 and 10824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10806 and 10824. First we will calculate the prime factors of 10806 and 10824.

Prime Factorization of 10806

Prime factors of 10806 are 2, 3, 1801. Prime factorization of 10806 in exponential form is:

10806 = 21 × 31 × 18011

Prime Factorization of 10824

Prime factors of 10824 are 2, 3, 11, 41. Prime factorization of 10824 in exponential form is:

10824 = 23 × 31 × 111 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 10806 and 10824.

LCM(10806,10824) = 23 × 31 × 18011 × 111 × 411
LCM(10806,10824) = 19494024