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What is the Least Common Multiple of 13722 and 13740?

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 13722 and 13740 is 31423380.

LCM(13722,13740) = 31423380

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Least Common Multiple of 13722 and 13740 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13722 and 13740, than apply into the LCM equation.

GCF(13722,13740) = 6
LCM(13722,13740) = ( 13722 × 13740) / 6
LCM(13722,13740) = 188540280 / 6
LCM(13722,13740) = 31423380

Least Common Multiple (LCM) of 13722 and 13740 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13722 and 13740. First we will calculate the prime factors of 13722 and 13740.

Prime Factorization of 13722

Prime factors of 13722 are 2, 3, 2287. Prime factorization of 13722 in exponential form is:

13722 = 21 × 31 × 22871

Prime Factorization of 13740

Prime factors of 13740 are 2, 3, 5, 229. Prime factorization of 13740 in exponential form is:

13740 = 22 × 31 × 51 × 2291

Now multiplying the highest exponent prime factors to calculate the LCM of 13722 and 13740.

LCM(13722,13740) = 22 × 31 × 22871 × 51 × 2291
LCM(13722,13740) = 31423380