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What is the Least Common Multiple of 2034 and 2045?

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 2034 and 2045 is 4159530.

LCM(2034,2045) = 4159530

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Least Common Multiple of 2034 and 2045 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2034 and 2045, than apply into the LCM equation.

GCF(2034,2045) = 1
LCM(2034,2045) = ( 2034 × 2045) / 1
LCM(2034,2045) = 4159530 / 1
LCM(2034,2045) = 4159530

Least Common Multiple (LCM) of 2034 and 2045 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2034 and 2045. First we will calculate the prime factors of 2034 and 2045.

Prime Factorization of 2034

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

2034 = 21 × 32 × 1131

Prime Factorization of 2045

Prime factors of 2045 are 5, 409. Prime factorization of 2045 in exponential form is:

2045 = 51 × 4091

Now multiplying the highest exponent prime factors to calculate the LCM of 2034 and 2045.

LCM(2034,2045) = 21 × 32 × 1131 × 51 × 4091
LCM(2034,2045) = 4159530