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What is the Least Common Multiple of 30993 and 31005?

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 30993 and 31005 is 320312655.

LCM(30993,31005) = 320312655

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Least Common Multiple of 30993 and 31005 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30993 and 31005, than apply into the LCM equation.

GCF(30993,31005) = 3
LCM(30993,31005) = ( 30993 × 31005) / 3
LCM(30993,31005) = 960937965 / 3
LCM(30993,31005) = 320312655

Least Common Multiple (LCM) of 30993 and 31005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30993 and 31005. First we will calculate the prime factors of 30993 and 31005.

Prime Factorization of 30993

Prime factors of 30993 are 3, 10331. Prime factorization of 30993 in exponential form is:

30993 = 31 × 103311

Prime Factorization of 31005

Prime factors of 31005 are 3, 5, 13, 53. Prime factorization of 31005 in exponential form is:

31005 = 32 × 51 × 131 × 531

Now multiplying the highest exponent prime factors to calculate the LCM of 30993 and 31005.

LCM(30993,31005) = 32 × 103311 × 51 × 131 × 531
LCM(30993,31005) = 320312655