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What is the Least Common Multiple of 13188 and 13205?

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 13188 and 13205 is 174147540.

LCM(13188,13205) = 174147540

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Least Common Multiple of 13188 and 13205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13188 and 13205, than apply into the LCM equation.

GCF(13188,13205) = 1
LCM(13188,13205) = ( 13188 × 13205) / 1
LCM(13188,13205) = 174147540 / 1
LCM(13188,13205) = 174147540

Least Common Multiple (LCM) of 13188 and 13205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13188 and 13205. First we will calculate the prime factors of 13188 and 13205.

Prime Factorization of 13188

Prime factors of 13188 are 2, 3, 7, 157. Prime factorization of 13188 in exponential form is:

13188 = 22 × 31 × 71 × 1571

Prime Factorization of 13205

Prime factors of 13205 are 5, 19, 139. Prime factorization of 13205 in exponential form is:

13205 = 51 × 191 × 1391

Now multiplying the highest exponent prime factors to calculate the LCM of 13188 and 13205.

LCM(13188,13205) = 22 × 31 × 71 × 1571 × 51 × 191 × 1391
LCM(13188,13205) = 174147540