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What is the Least Common Multiple of 2104 and 2108?

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 2108 is 1108808.

LCM(2104,2108) = 1108808

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Least Common Multiple of 2104 and 2108 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 2108, than apply into the LCM equation.

GCF(2104,2108) = 4
LCM(2104,2108) = ( 2104 × 2108) / 4
LCM(2104,2108) = 4435232 / 4
LCM(2104,2108) = 1108808

Least Common Multiple (LCM) of 2104 and 2108 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2104 and 2108. First we will calculate the prime factors of 2104 and 2108.

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 2108

Prime factors of 2108 are 2, 17, 31. Prime factorization of 2108 in exponential form is:

2108 = 22 × 171 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 2104 and 2108.

LCM(2104,2108) = 23 × 2631 × 171 × 311
LCM(2104,2108) = 1108808