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What is the Least Common Multiple of 9680 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 9680 and 9700 is 4694800.

LCM(9680,9700) = 4694800

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Least Common Multiple of 9680 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 9680 and 9700, than apply into the LCM equation.

GCF(9680,9700) = 20
LCM(9680,9700) = ( 9680 × 9700) / 20
LCM(9680,9700) = 93896000 / 20
LCM(9680,9700) = 4694800

Least Common Multiple (LCM) of 9680 and 9700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9680 and 9700. First we will calculate the prime factors of 9680 and 9700.

Prime Factorization of 9680

Prime factors of 9680 are 2, 5, 11. Prime factorization of 9680 in exponential form is:

9680 = 24 × 51 × 112

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 9680 and 9700.

LCM(9680,9700) = 24 × 52 × 112 × 971
LCM(9680,9700) = 4694800