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What is the Least Common Multiple of 13661 and 13680?

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 13661 and 13680 is 9835920.

LCM(13661,13680) = 9835920

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Least Common Multiple of 13661 and 13680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13661 and 13680, than apply into the LCM equation.

GCF(13661,13680) = 19
LCM(13661,13680) = ( 13661 × 13680) / 19
LCM(13661,13680) = 186882480 / 19
LCM(13661,13680) = 9835920

Least Common Multiple (LCM) of 13661 and 13680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13661 and 13680. First we will calculate the prime factors of 13661 and 13680.

Prime Factorization of 13661

Prime factors of 13661 are 19, 719. Prime factorization of 13661 in exponential form is:

13661 = 191 × 7191

Prime Factorization of 13680

Prime factors of 13680 are 2, 3, 5, 19. Prime factorization of 13680 in exponential form is:

13680 = 24 × 32 × 51 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 13661 and 13680.

LCM(13661,13680) = 191 × 7191 × 24 × 32 × 51
LCM(13661,13680) = 9835920