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What is the Least Common Multiple of 13523 and 13542?

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 13523 and 13542 is 183128466.

LCM(13523,13542) = 183128466

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Least Common Multiple of 13523 and 13542 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13523 and 13542, than apply into the LCM equation.

GCF(13523,13542) = 1
LCM(13523,13542) = ( 13523 × 13542) / 1
LCM(13523,13542) = 183128466 / 1
LCM(13523,13542) = 183128466

Least Common Multiple (LCM) of 13523 and 13542 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13523 and 13542. First we will calculate the prime factors of 13523 and 13542.

Prime Factorization of 13523

Prime factors of 13523 are 13523. Prime factorization of 13523 in exponential form is:

13523 = 135231

Prime Factorization of 13542

Prime factors of 13542 are 2, 3, 37, 61. Prime factorization of 13542 in exponential form is:

13542 = 21 × 31 × 371 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 13523 and 13542.

LCM(13523,13542) = 135231 × 21 × 31 × 371 × 611
LCM(13523,13542) = 183128466