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What is the Least Common Multiple of 13565 and 13578?

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 13565 and 13578 is 184185570.

LCM(13565,13578) = 184185570

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Least Common Multiple of 13565 and 13578 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13565 and 13578, than apply into the LCM equation.

GCF(13565,13578) = 1
LCM(13565,13578) = ( 13565 × 13578) / 1
LCM(13565,13578) = 184185570 / 1
LCM(13565,13578) = 184185570

Least Common Multiple (LCM) of 13565 and 13578 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13565 and 13578. First we will calculate the prime factors of 13565 and 13578.

Prime Factorization of 13565

Prime factors of 13565 are 5, 2713. Prime factorization of 13565 in exponential form is:

13565 = 51 × 27131

Prime Factorization of 13578

Prime factors of 13578 are 2, 3, 31, 73. Prime factorization of 13578 in exponential form is:

13578 = 21 × 31 × 311 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 13565 and 13578.

LCM(13565,13578) = 51 × 27131 × 21 × 31 × 311 × 731
LCM(13565,13578) = 184185570