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What is the Least Common Multiple of 13707 and 13725?

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 13707 and 13725 is 20903175.

LCM(13707,13725) = 20903175

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Least Common Multiple of 13707 and 13725 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13707 and 13725, than apply into the LCM equation.

GCF(13707,13725) = 9
LCM(13707,13725) = ( 13707 × 13725) / 9
LCM(13707,13725) = 188128575 / 9
LCM(13707,13725) = 20903175

Least Common Multiple (LCM) of 13707 and 13725 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13707 and 13725. First we will calculate the prime factors of 13707 and 13725.

Prime Factorization of 13707

Prime factors of 13707 are 3, 1523. Prime factorization of 13707 in exponential form is:

13707 = 32 × 15231

Prime Factorization of 13725

Prime factors of 13725 are 3, 5, 61. Prime factorization of 13725 in exponential form is:

13725 = 32 × 52 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 13707 and 13725.

LCM(13707,13725) = 32 × 15231 × 52 × 611
LCM(13707,13725) = 20903175