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What is the Least Common Multiple of 310 and 319?

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 310 and 319 is 98890.

LCM(310,319) = 98890

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Least Common Multiple of 310 and 319 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 310 and 319, than apply into the LCM equation.

GCF(310,319) = 1
LCM(310,319) = ( 310 × 319) / 1
LCM(310,319) = 98890 / 1
LCM(310,319) = 98890

Least Common Multiple (LCM) of 310 and 319 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 310 and 319. First we will calculate the prime factors of 310 and 319.

Prime Factorization of 310

Prime factors of 310 are 2, 5, 31. Prime factorization of 310 in exponential form is:

310 = 21 × 51 × 311

Prime Factorization of 319

Prime factors of 319 are 11, 29. Prime factorization of 319 in exponential form is:

319 = 111 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 310 and 319.

LCM(310,319) = 21 × 51 × 311 × 111 × 291
LCM(310,319) = 98890