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What is the Least Common Multiple of 305 and 310?

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 305 and 310 is 18910.

LCM(305,310) = 18910

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Least Common Multiple of 305 and 310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 305 and 310, than apply into the LCM equation.

GCF(305,310) = 5
LCM(305,310) = ( 305 × 310) / 5
LCM(305,310) = 94550 / 5
LCM(305,310) = 18910

Least Common Multiple (LCM) of 305 and 310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 305 and 310. First we will calculate the prime factors of 305 and 310.

Prime Factorization of 305

Prime factors of 305 are 5, 61. Prime factorization of 305 in exponential form is:

305 = 51 × 611

Prime Factorization of 310

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

310 = 21 × 51 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 305 and 310.

LCM(305,310) = 51 × 611 × 21 × 311
LCM(305,310) = 18910