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What is the Least Common Multiple of 13653 and 13662?

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 13653 and 13662 is 20725254.

LCM(13653,13662) = 20725254

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Least Common Multiple of 13653 and 13662 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13653 and 13662, than apply into the LCM equation.

GCF(13653,13662) = 9
LCM(13653,13662) = ( 13653 × 13662) / 9
LCM(13653,13662) = 186527286 / 9
LCM(13653,13662) = 20725254

Least Common Multiple (LCM) of 13653 and 13662 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13653 and 13662. First we will calculate the prime factors of 13653 and 13662.

Prime Factorization of 13653

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

13653 = 32 × 371 × 411

Prime Factorization of 13662

Prime factors of 13662 are 2, 3, 11, 23. Prime factorization of 13662 in exponential form is:

13662 = 21 × 33 × 111 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 13653 and 13662.

LCM(13653,13662) = 33 × 371 × 411 × 21 × 111 × 231
LCM(13653,13662) = 20725254