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What is the Least Common Multiple of 15665 and 15678?

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 15665 and 15678 is 18891990.

LCM(15665,15678) = 18891990

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Least Common Multiple of 15665 and 15678 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15665 and 15678, than apply into the LCM equation.

GCF(15665,15678) = 13
LCM(15665,15678) = ( 15665 × 15678) / 13
LCM(15665,15678) = 245595870 / 13
LCM(15665,15678) = 18891990

Least Common Multiple (LCM) of 15665 and 15678 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15665 and 15678. First we will calculate the prime factors of 15665 and 15678.

Prime Factorization of 15665

Prime factors of 15665 are 5, 13, 241. Prime factorization of 15665 in exponential form is:

15665 = 51 × 131 × 2411

Prime Factorization of 15678

Prime factors of 15678 are 2, 3, 13, 67. Prime factorization of 15678 in exponential form is:

15678 = 21 × 32 × 131 × 671

Now multiplying the highest exponent prime factors to calculate the LCM of 15665 and 15678.

LCM(15665,15678) = 51 × 131 × 2411 × 21 × 32 × 671
LCM(15665,15678) = 18891990