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What is the Least Common Multiple of 67678 and 67697?

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 67678 and 67697 is 241136714.

LCM(67678,67697) = 241136714

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Least Common Multiple of 67678 and 67697 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67678 and 67697, than apply into the LCM equation.

GCF(67678,67697) = 19
LCM(67678,67697) = ( 67678 × 67697) / 19
LCM(67678,67697) = 4581597566 / 19
LCM(67678,67697) = 241136714

Least Common Multiple (LCM) of 67678 and 67697 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67678 and 67697. First we will calculate the prime factors of 67678 and 67697.

Prime Factorization of 67678

Prime factors of 67678 are 2, 13, 19, 137. Prime factorization of 67678 in exponential form is:

67678 = 21 × 131 × 191 × 1371

Prime Factorization of 67697

Prime factors of 67697 are 7, 19, 509. Prime factorization of 67697 in exponential form is:

67697 = 71 × 191 × 5091

Now multiplying the highest exponent prime factors to calculate the LCM of 67678 and 67697.

LCM(67678,67697) = 21 × 131 × 191 × 1371 × 71 × 5091
LCM(67678,67697) = 241136714