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What is the Least Common Multiple of 10678 and 10682?

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 10678 and 10682 is 57031198.

LCM(10678,10682) = 57031198

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Least Common Multiple of 10678 and 10682 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10678 and 10682, than apply into the LCM equation.

GCF(10678,10682) = 2
LCM(10678,10682) = ( 10678 × 10682) / 2
LCM(10678,10682) = 114062396 / 2
LCM(10678,10682) = 57031198

Least Common Multiple (LCM) of 10678 and 10682 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10678 and 10682. First we will calculate the prime factors of 10678 and 10682.

Prime Factorization of 10678

Prime factors of 10678 are 2, 19, 281. Prime factorization of 10678 in exponential form is:

10678 = 21 × 191 × 2811

Prime Factorization of 10682

Prime factors of 10682 are 2, 7, 109. Prime factorization of 10682 in exponential form is:

10682 = 21 × 72 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 10678 and 10682.

LCM(10678,10682) = 21 × 191 × 2811 × 72 × 1091
LCM(10678,10682) = 57031198