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What is the Least Common Multiple of 9685 and 9700?

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 9685 and 9700 is 18788900.

LCM(9685,9700) = 18788900

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Least Common Multiple of 9685 and 9700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9685 and 9700, than apply into the LCM equation.

GCF(9685,9700) = 5
LCM(9685,9700) = ( 9685 × 9700) / 5
LCM(9685,9700) = 93944500 / 5
LCM(9685,9700) = 18788900

Least Common Multiple (LCM) of 9685 and 9700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9685 and 9700. First we will calculate the prime factors of 9685 and 9700.

Prime Factorization of 9685

Prime factors of 9685 are 5, 13, 149. Prime factorization of 9685 in exponential form is:

9685 = 51 × 131 × 1491

Prime Factorization of 9700

Prime factors of 9700 are 2, 5, 97. Prime factorization of 9700 in exponential form is:

9700 = 22 × 52 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 9685 and 9700.

LCM(9685,9700) = 52 × 131 × 1491 × 22 × 971
LCM(9685,9700) = 18788900