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What is the Least Common Multiple of 7686 and 7706?

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 7686 and 7706 is 29614158.

LCM(7686,7706) = 29614158

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Least Common Multiple of 7686 and 7706 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7686 and 7706, than apply into the LCM equation.

GCF(7686,7706) = 2
LCM(7686,7706) = ( 7686 × 7706) / 2
LCM(7686,7706) = 59228316 / 2
LCM(7686,7706) = 29614158

Least Common Multiple (LCM) of 7686 and 7706 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7686 and 7706. First we will calculate the prime factors of 7686 and 7706.

Prime Factorization of 7686

Prime factors of 7686 are 2, 3, 7, 61. Prime factorization of 7686 in exponential form is:

7686 = 21 × 32 × 71 × 611

Prime Factorization of 7706

Prime factors of 7706 are 2, 3853. Prime factorization of 7706 in exponential form is:

7706 = 21 × 38531

Now multiplying the highest exponent prime factors to calculate the LCM of 7686 and 7706.

LCM(7686,7706) = 21 × 32 × 71 × 611 × 38531
LCM(7686,7706) = 29614158