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What is the Least Common Multiple of 9680 and 9684?

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 9684 is 23435280.

LCM(9680,9684) = 23435280

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Least Common Multiple of 9680 and 9684 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 9684, than apply into the LCM equation.

GCF(9680,9684) = 4
LCM(9680,9684) = ( 9680 × 9684) / 4
LCM(9680,9684) = 93741120 / 4
LCM(9680,9684) = 23435280

Least Common Multiple (LCM) of 9680 and 9684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9680 and 9684. First we will calculate the prime factors of 9680 and 9684.

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 9684

Prime factors of 9684 are 2, 3, 269. Prime factorization of 9684 in exponential form is:

9684 = 22 × 32 × 2691

Now multiplying the highest exponent prime factors to calculate the LCM of 9680 and 9684.

LCM(9680,9684) = 24 × 51 × 112 × 32 × 2691
LCM(9680,9684) = 23435280