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What is the Least Common Multiple of 13502 and 13516?

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 13502 and 13516 is 91246516.

LCM(13502,13516) = 91246516

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Least Common Multiple of 13502 and 13516 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13502 and 13516, than apply into the LCM equation.

GCF(13502,13516) = 2
LCM(13502,13516) = ( 13502 × 13516) / 2
LCM(13502,13516) = 182493032 / 2
LCM(13502,13516) = 91246516

Least Common Multiple (LCM) of 13502 and 13516 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13502 and 13516. First we will calculate the prime factors of 13502 and 13516.

Prime Factorization of 13502

Prime factors of 13502 are 2, 43, 157. Prime factorization of 13502 in exponential form is:

13502 = 21 × 431 × 1571

Prime Factorization of 13516

Prime factors of 13516 are 2, 31, 109. Prime factorization of 13516 in exponential form is:

13516 = 22 × 311 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 13502 and 13516.

LCM(13502,13516) = 22 × 431 × 1571 × 311 × 1091
LCM(13502,13516) = 91246516