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What is the Least Common Multiple of 7684 and 7700?

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 7684 and 7700 is 14791700.

LCM(7684,7700) = 14791700

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Least Common Multiple of 7684 and 7700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7684 and 7700, than apply into the LCM equation.

GCF(7684,7700) = 4
LCM(7684,7700) = ( 7684 × 7700) / 4
LCM(7684,7700) = 59166800 / 4
LCM(7684,7700) = 14791700

Least Common Multiple (LCM) of 7684 and 7700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7684 and 7700. First we will calculate the prime factors of 7684 and 7700.

Prime Factorization of 7684

Prime factors of 7684 are 2, 17, 113. Prime factorization of 7684 in exponential form is:

7684 = 22 × 171 × 1131

Prime Factorization of 7700

Prime factors of 7700 are 2, 5, 7, 11. Prime factorization of 7700 in exponential form is:

7700 = 22 × 52 × 71 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 7684 and 7700.

LCM(7684,7700) = 22 × 171 × 1131 × 52 × 71 × 111
LCM(7684,7700) = 14791700