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What is the Least Common Multiple of 13609 and 13624?

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 13609 and 13624 is 185409016.

LCM(13609,13624) = 185409016

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Least Common Multiple of 13609 and 13624 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13609 and 13624, than apply into the LCM equation.

GCF(13609,13624) = 1
LCM(13609,13624) = ( 13609 × 13624) / 1
LCM(13609,13624) = 185409016 / 1
LCM(13609,13624) = 185409016

Least Common Multiple (LCM) of 13609 and 13624 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13609 and 13624. First we will calculate the prime factors of 13609 and 13624.

Prime Factorization of 13609

Prime factors of 13609 are 31, 439. Prime factorization of 13609 in exponential form is:

13609 = 311 × 4391

Prime Factorization of 13624

Prime factors of 13624 are 2, 13, 131. Prime factorization of 13624 in exponential form is:

13624 = 23 × 131 × 1311

Now multiplying the highest exponent prime factors to calculate the LCM of 13609 and 13624.

LCM(13609,13624) = 311 × 4391 × 23 × 131 × 1311
LCM(13609,13624) = 185409016