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What is the Least Common Multiple of 2174 and 2184?

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 2174 and 2184 is 2374008.

LCM(2174,2184) = 2374008

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Least Common Multiple of 2174 and 2184 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2174 and 2184, than apply into the LCM equation.

GCF(2174,2184) = 2
LCM(2174,2184) = ( 2174 × 2184) / 2
LCM(2174,2184) = 4748016 / 2
LCM(2174,2184) = 2374008

Least Common Multiple (LCM) of 2174 and 2184 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2174 and 2184. First we will calculate the prime factors of 2174 and 2184.

Prime Factorization of 2174

Prime factors of 2174 are 2, 1087. Prime factorization of 2174 in exponential form is:

2174 = 21 × 10871

Prime Factorization of 2184

Prime factors of 2184 are 2, 3, 7, 13. Prime factorization of 2184 in exponential form is:

2184 = 23 × 31 × 71 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 2174 and 2184.

LCM(2174,2184) = 23 × 10871 × 31 × 71 × 131
LCM(2174,2184) = 2374008