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What is the Least Common Multiple of 13600 and 13614?

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 13600 and 13614 is 92575200.

LCM(13600,13614) = 92575200

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Least Common Multiple of 13600 and 13614 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13600 and 13614, than apply into the LCM equation.

GCF(13600,13614) = 2
LCM(13600,13614) = ( 13600 × 13614) / 2
LCM(13600,13614) = 185150400 / 2
LCM(13600,13614) = 92575200

Least Common Multiple (LCM) of 13600 and 13614 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13600 and 13614. First we will calculate the prime factors of 13600 and 13614.

Prime Factorization of 13600

Prime factors of 13600 are 2, 5, 17. Prime factorization of 13600 in exponential form is:

13600 = 25 × 52 × 171

Prime Factorization of 13614

Prime factors of 13614 are 2, 3, 2269. Prime factorization of 13614 in exponential form is:

13614 = 21 × 31 × 22691

Now multiplying the highest exponent prime factors to calculate the LCM of 13600 and 13614.

LCM(13600,13614) = 25 × 52 × 171 × 31 × 22691
LCM(13600,13614) = 92575200