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What is the Least Common Multiple of 13624 and 13640?

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 13624 and 13640 is 23228920.

LCM(13624,13640) = 23228920

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Least Common Multiple of 13624 and 13640 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13624 and 13640, than apply into the LCM equation.

GCF(13624,13640) = 8
LCM(13624,13640) = ( 13624 × 13640) / 8
LCM(13624,13640) = 185831360 / 8
LCM(13624,13640) = 23228920

Least Common Multiple (LCM) of 13624 and 13640 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13624 and 13640. First we will calculate the prime factors of 13624 and 13640.

Prime Factorization of 13624

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

13624 = 23 × 131 × 1311

Prime Factorization of 13640

Prime factors of 13640 are 2, 5, 11, 31. Prime factorization of 13640 in exponential form is:

13640 = 23 × 51 × 111 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 13624 and 13640.

LCM(13624,13640) = 23 × 131 × 1311 × 51 × 111 × 311
LCM(13624,13640) = 23228920