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What is the Least Common Multiple of 13746 and 13759?

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 13746 and 13759 is 189131214.

LCM(13746,13759) = 189131214

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Least Common Multiple of 13746 and 13759 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13746 and 13759, than apply into the LCM equation.

GCF(13746,13759) = 1
LCM(13746,13759) = ( 13746 × 13759) / 1
LCM(13746,13759) = 189131214 / 1
LCM(13746,13759) = 189131214

Least Common Multiple (LCM) of 13746 and 13759 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13746 and 13759. First we will calculate the prime factors of 13746 and 13759.

Prime Factorization of 13746

Prime factors of 13746 are 2, 3, 29, 79. Prime factorization of 13746 in exponential form is:

13746 = 21 × 31 × 291 × 791

Prime Factorization of 13759

Prime factors of 13759 are 13759. Prime factorization of 13759 in exponential form is:

13759 = 137591

Now multiplying the highest exponent prime factors to calculate the LCM of 13746 and 13759.

LCM(13746,13759) = 21 × 31 × 291 × 791 × 137591
LCM(13746,13759) = 189131214