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What is the Least Common Multiple of 13496 and 13500?

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 13496 and 13500 is 45549000.

LCM(13496,13500) = 45549000

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Least Common Multiple of 13496 and 13500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13496 and 13500, than apply into the LCM equation.

GCF(13496,13500) = 4
LCM(13496,13500) = ( 13496 × 13500) / 4
LCM(13496,13500) = 182196000 / 4
LCM(13496,13500) = 45549000

Least Common Multiple (LCM) of 13496 and 13500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13496 and 13500. First we will calculate the prime factors of 13496 and 13500.

Prime Factorization of 13496

Prime factors of 13496 are 2, 7, 241. Prime factorization of 13496 in exponential form is:

13496 = 23 × 71 × 2411

Prime Factorization of 13500

Prime factors of 13500 are 2, 3, 5. Prime factorization of 13500 in exponential form is:

13500 = 22 × 33 × 53

Now multiplying the highest exponent prime factors to calculate the LCM of 13496 and 13500.

LCM(13496,13500) = 23 × 71 × 2411 × 33 × 53
LCM(13496,13500) = 45549000