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What is the Least Common Multiple of 13670 and 13690?

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 13670 and 13690 is 18714230.

LCM(13670,13690) = 18714230

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Least Common Multiple of 13670 and 13690 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13670 and 13690, than apply into the LCM equation.

GCF(13670,13690) = 10
LCM(13670,13690) = ( 13670 × 13690) / 10
LCM(13670,13690) = 187142300 / 10
LCM(13670,13690) = 18714230

Least Common Multiple (LCM) of 13670 and 13690 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13670 and 13690. First we will calculate the prime factors of 13670 and 13690.

Prime Factorization of 13670

Prime factors of 13670 are 2, 5, 1367. Prime factorization of 13670 in exponential form is:

13670 = 21 × 51 × 13671

Prime Factorization of 13690

Prime factors of 13690 are 2, 5, 37. Prime factorization of 13690 in exponential form is:

13690 = 21 × 51 × 372

Now multiplying the highest exponent prime factors to calculate the LCM of 13670 and 13690.

LCM(13670,13690) = 21 × 51 × 13671 × 372
LCM(13670,13690) = 18714230