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What is the Least Common Multiple of 13690 and 13705?

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 13690 and 13705 is 37524290.

LCM(13690,13705) = 37524290

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Least Common Multiple of 13690 and 13705 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13690 and 13705, than apply into the LCM equation.

GCF(13690,13705) = 5
LCM(13690,13705) = ( 13690 × 13705) / 5
LCM(13690,13705) = 187621450 / 5
LCM(13690,13705) = 37524290

Least Common Multiple (LCM) of 13690 and 13705 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13690 and 13705. First we will calculate the prime factors of 13690 and 13705.

Prime Factorization of 13690

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

13690 = 21 × 51 × 372

Prime Factorization of 13705

Prime factors of 13705 are 5, 2741. Prime factorization of 13705 in exponential form is:

13705 = 51 × 27411

Now multiplying the highest exponent prime factors to calculate the LCM of 13690 and 13705.

LCM(13690,13705) = 21 × 51 × 372 × 27411
LCM(13690,13705) = 37524290