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What is the Least Common Multiple of 10696 and 10704?

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 10696 and 10704 is 14311248.

LCM(10696,10704) = 14311248

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Least Common Multiple of 10696 and 10704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10696 and 10704, than apply into the LCM equation.

GCF(10696,10704) = 8
LCM(10696,10704) = ( 10696 × 10704) / 8
LCM(10696,10704) = 114489984 / 8
LCM(10696,10704) = 14311248

Least Common Multiple (LCM) of 10696 and 10704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10696 and 10704. First we will calculate the prime factors of 10696 and 10704.

Prime Factorization of 10696

Prime factors of 10696 are 2, 7, 191. Prime factorization of 10696 in exponential form is:

10696 = 23 × 71 × 1911

Prime Factorization of 10704

Prime factors of 10704 are 2, 3, 223. Prime factorization of 10704 in exponential form is:

10704 = 24 × 31 × 2231

Now multiplying the highest exponent prime factors to calculate the LCM of 10696 and 10704.

LCM(10696,10704) = 24 × 71 × 1911 × 31 × 2231
LCM(10696,10704) = 14311248