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What is the Least Common Multiple of 54096 and 54110?

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 54096 and 54110 is 209081040.

LCM(54096,54110) = 209081040

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Least Common Multiple of 54096 and 54110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54096 and 54110, than apply into the LCM equation.

GCF(54096,54110) = 14
LCM(54096,54110) = ( 54096 × 54110) / 14
LCM(54096,54110) = 2927134560 / 14
LCM(54096,54110) = 209081040

Least Common Multiple (LCM) of 54096 and 54110 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54096 and 54110. First we will calculate the prime factors of 54096 and 54110.

Prime Factorization of 54096

Prime factors of 54096 are 2, 3, 7, 23. Prime factorization of 54096 in exponential form is:

54096 = 24 × 31 × 72 × 231

Prime Factorization of 54110

Prime factors of 54110 are 2, 5, 7, 773. Prime factorization of 54110 in exponential form is:

54110 = 21 × 51 × 71 × 7731

Now multiplying the highest exponent prime factors to calculate the LCM of 54096 and 54110.

LCM(54096,54110) = 24 × 31 × 72 × 231 × 51 × 7731
LCM(54096,54110) = 209081040