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What is the Least Common Multiple of 2104 and 2122?

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 2104 and 2122 is 2232344.

LCM(2104,2122) = 2232344

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Least Common Multiple of 2104 and 2122 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2104 and 2122, than apply into the LCM equation.

GCF(2104,2122) = 2
LCM(2104,2122) = ( 2104 × 2122) / 2
LCM(2104,2122) = 4464688 / 2
LCM(2104,2122) = 2232344

Least Common Multiple (LCM) of 2104 and 2122 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2104 and 2122. First we will calculate the prime factors of 2104 and 2122.

Prime Factorization of 2104

Prime factors of 2104 are 2, 263. Prime factorization of 2104 in exponential form is:

2104 = 23 × 2631

Prime Factorization of 2122

Prime factors of 2122 are 2, 1061. Prime factorization of 2122 in exponential form is:

2122 = 21 × 10611

Now multiplying the highest exponent prime factors to calculate the LCM of 2104 and 2122.

LCM(2104,2122) = 23 × 2631 × 10611
LCM(2104,2122) = 2232344