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What is the Least Common Multiple of 19689 and 19700?

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 19689 and 19700 is 387873300.

LCM(19689,19700) = 387873300

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Least Common Multiple of 19689 and 19700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19689 and 19700, than apply into the LCM equation.

GCF(19689,19700) = 1
LCM(19689,19700) = ( 19689 × 19700) / 1
LCM(19689,19700) = 387873300 / 1
LCM(19689,19700) = 387873300

Least Common Multiple (LCM) of 19689 and 19700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19689 and 19700. First we will calculate the prime factors of 19689 and 19700.

Prime Factorization of 19689

Prime factors of 19689 are 3, 6563. Prime factorization of 19689 in exponential form is:

19689 = 31 × 65631

Prime Factorization of 19700

Prime factors of 19700 are 2, 5, 197. Prime factorization of 19700 in exponential form is:

19700 = 22 × 52 × 1971

Now multiplying the highest exponent prime factors to calculate the LCM of 19689 and 19700.

LCM(19689,19700) = 31 × 65631 × 22 × 52 × 1971
LCM(19689,19700) = 387873300