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What is the Least Common Multiple of 30667 and 30674?

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 30667 and 30674 is 134382794.

LCM(30667,30674) = 134382794

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Least Common Multiple of 30667 and 30674 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30667 and 30674, than apply into the LCM equation.

GCF(30667,30674) = 7
LCM(30667,30674) = ( 30667 × 30674) / 7
LCM(30667,30674) = 940679558 / 7
LCM(30667,30674) = 134382794

Least Common Multiple (LCM) of 30667 and 30674 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30667 and 30674. First we will calculate the prime factors of 30667 and 30674.

Prime Factorization of 30667

Prime factors of 30667 are 7, 13, 337. Prime factorization of 30667 in exponential form is:

30667 = 71 × 131 × 3371

Prime Factorization of 30674

Prime factors of 30674 are 2, 7, 313. Prime factorization of 30674 in exponential form is:

30674 = 21 × 72 × 3131

Now multiplying the highest exponent prime factors to calculate the LCM of 30667 and 30674.

LCM(30667,30674) = 72 × 131 × 3371 × 21 × 3131
LCM(30667,30674) = 134382794