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What is the Least Common Multiple of 2015 and 2034?

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 2015 and 2034 is 4098510.

LCM(2015,2034) = 4098510

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Least Common Multiple of 2015 and 2034 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2015 and 2034, than apply into the LCM equation.

GCF(2015,2034) = 1
LCM(2015,2034) = ( 2015 × 2034) / 1
LCM(2015,2034) = 4098510 / 1
LCM(2015,2034) = 4098510

Least Common Multiple (LCM) of 2015 and 2034 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2015 and 2034. First we will calculate the prime factors of 2015 and 2034.

Prime Factorization of 2015

Prime factors of 2015 are 5, 13, 31. Prime factorization of 2015 in exponential form is:

2015 = 51 × 131 × 311

Prime Factorization of 2034

Prime factors of 2034 are 2, 3, 113. Prime factorization of 2034 in exponential form is:

2034 = 21 × 32 × 1131

Now multiplying the highest exponent prime factors to calculate the LCM of 2015 and 2034.

LCM(2015,2034) = 51 × 131 × 311 × 21 × 32 × 1131
LCM(2015,2034) = 4098510