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What is the Least Common Multiple of 13644 and 13653?

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 13644 and 13653 is 20697948.

LCM(13644,13653) = 20697948

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Least Common Multiple of 13644 and 13653 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13644 and 13653, than apply into the LCM equation.

GCF(13644,13653) = 9
LCM(13644,13653) = ( 13644 × 13653) / 9
LCM(13644,13653) = 186281532 / 9
LCM(13644,13653) = 20697948

Least Common Multiple (LCM) of 13644 and 13653 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13644 and 13653. First we will calculate the prime factors of 13644 and 13653.

Prime Factorization of 13644

Prime factors of 13644 are 2, 3, 379. Prime factorization of 13644 in exponential form is:

13644 = 22 × 32 × 3791

Prime Factorization of 13653

Prime factors of 13653 are 3, 37, 41. Prime factorization of 13653 in exponential form is:

13653 = 32 × 371 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 13644 and 13653.

LCM(13644,13653) = 22 × 32 × 3791 × 371 × 411
LCM(13644,13653) = 20697948