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What is the Least Common Multiple of 55104 and 55116?

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 55104 and 55116 is 253092672.

LCM(55104,55116) = 253092672

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Least Common Multiple of 55104 and 55116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55104 and 55116, than apply into the LCM equation.

GCF(55104,55116) = 12
LCM(55104,55116) = ( 55104 × 55116) / 12
LCM(55104,55116) = 3037112064 / 12
LCM(55104,55116) = 253092672

Least Common Multiple (LCM) of 55104 and 55116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55104 and 55116. First we will calculate the prime factors of 55104 and 55116.

Prime Factorization of 55104

Prime factors of 55104 are 2, 3, 7, 41. Prime factorization of 55104 in exponential form is:

55104 = 26 × 31 × 71 × 411

Prime Factorization of 55116

Prime factors of 55116 are 2, 3, 1531. Prime factorization of 55116 in exponential form is:

55116 = 22 × 32 × 15311

Now multiplying the highest exponent prime factors to calculate the LCM of 55104 and 55116.

LCM(55104,55116) = 26 × 32 × 71 × 411 × 15311
LCM(55104,55116) = 253092672