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What is the Least Common Multiple of 13629 and 13648?

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 13629 and 13648 is 186008592.

LCM(13629,13648) = 186008592

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Least Common Multiple of 13629 and 13648 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13629 and 13648, than apply into the LCM equation.

GCF(13629,13648) = 1
LCM(13629,13648) = ( 13629 × 13648) / 1
LCM(13629,13648) = 186008592 / 1
LCM(13629,13648) = 186008592

Least Common Multiple (LCM) of 13629 and 13648 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13629 and 13648. First we will calculate the prime factors of 13629 and 13648.

Prime Factorization of 13629

Prime factors of 13629 are 3, 7, 11, 59. Prime factorization of 13629 in exponential form is:

13629 = 31 × 71 × 111 × 591

Prime Factorization of 13648

Prime factors of 13648 are 2, 853. Prime factorization of 13648 in exponential form is:

13648 = 24 × 8531

Now multiplying the highest exponent prime factors to calculate the LCM of 13629 and 13648.

LCM(13629,13648) = 31 × 71 × 111 × 591 × 24 × 8531
LCM(13629,13648) = 186008592