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What is the Least Common Multiple of 30985 and 31000?

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 30985 and 31000 is 192107000.

LCM(30985,31000) = 192107000

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Least Common Multiple of 30985 and 31000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30985 and 31000, than apply into the LCM equation.

GCF(30985,31000) = 5
LCM(30985,31000) = ( 30985 × 31000) / 5
LCM(30985,31000) = 960535000 / 5
LCM(30985,31000) = 192107000

Least Common Multiple (LCM) of 30985 and 31000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30985 and 31000. First we will calculate the prime factors of 30985 and 31000.

Prime Factorization of 30985

Prime factors of 30985 are 5, 6197. Prime factorization of 30985 in exponential form is:

30985 = 51 × 61971

Prime Factorization of 31000

Prime factors of 31000 are 2, 5, 31. Prime factorization of 31000 in exponential form is:

31000 = 23 × 53 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 30985 and 31000.

LCM(30985,31000) = 53 × 61971 × 23 × 311
LCM(30985,31000) = 192107000