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What is the Least Common Multiple of 2104 and 2116?

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 2116 is 1113016.

LCM(2104,2116) = 1113016

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Least Common Multiple of 2104 and 2116 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 2116, than apply into the LCM equation.

GCF(2104,2116) = 4
LCM(2104,2116) = ( 2104 × 2116) / 4
LCM(2104,2116) = 4452064 / 4
LCM(2104,2116) = 1113016

Least Common Multiple (LCM) of 2104 and 2116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2104 and 2116. First we will calculate the prime factors of 2104 and 2116.

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 2116

Prime factors of 2116 are 2, 23. Prime factorization of 2116 in exponential form is:

2116 = 22 × 232

Now multiplying the highest exponent prime factors to calculate the LCM of 2104 and 2116.

LCM(2104,2116) = 23 × 2631 × 232
LCM(2104,2116) = 1113016