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What is the Least Common Multiple of 2289 and 2300?

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 2289 and 2300 is 5264700.

LCM(2289,2300) = 5264700

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Least Common Multiple of 2289 and 2300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2289 and 2300, than apply into the LCM equation.

GCF(2289,2300) = 1
LCM(2289,2300) = ( 2289 × 2300) / 1
LCM(2289,2300) = 5264700 / 1
LCM(2289,2300) = 5264700

Least Common Multiple (LCM) of 2289 and 2300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2289 and 2300. First we will calculate the prime factors of 2289 and 2300.

Prime Factorization of 2289

Prime factors of 2289 are 3, 7, 109. Prime factorization of 2289 in exponential form is:

2289 = 31 × 71 × 1091

Prime Factorization of 2300

Prime factors of 2300 are 2, 5, 23. Prime factorization of 2300 in exponential form is:

2300 = 22 × 52 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 2289 and 2300.

LCM(2289,2300) = 31 × 71 × 1091 × 22 × 52 × 231
LCM(2289,2300) = 5264700