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What is the Least Common Multiple of 7826 and 7842?

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 7826 and 7842 is 30685746.

LCM(7826,7842) = 30685746

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Least Common Multiple of 7826 and 7842 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7826 and 7842, than apply into the LCM equation.

GCF(7826,7842) = 2
LCM(7826,7842) = ( 7826 × 7842) / 2
LCM(7826,7842) = 61371492 / 2
LCM(7826,7842) = 30685746

Least Common Multiple (LCM) of 7826 and 7842 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7826 and 7842. First we will calculate the prime factors of 7826 and 7842.

Prime Factorization of 7826

Prime factors of 7826 are 2, 7, 13, 43. Prime factorization of 7826 in exponential form is:

7826 = 21 × 71 × 131 × 431

Prime Factorization of 7842

Prime factors of 7842 are 2, 3, 1307. Prime factorization of 7842 in exponential form is:

7842 = 21 × 31 × 13071

Now multiplying the highest exponent prime factors to calculate the LCM of 7826 and 7842.

LCM(7826,7842) = 21 × 71 × 131 × 431 × 31 × 13071
LCM(7826,7842) = 30685746