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What is the Least Common Multiple of 10298 and 10304?

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 10298 and 10304 is 53055296.

LCM(10298,10304) = 53055296

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Least Common Multiple of 10298 and 10304 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10298 and 10304, than apply into the LCM equation.

GCF(10298,10304) = 2
LCM(10298,10304) = ( 10298 × 10304) / 2
LCM(10298,10304) = 106110592 / 2
LCM(10298,10304) = 53055296

Least Common Multiple (LCM) of 10298 and 10304 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10298 and 10304. First we will calculate the prime factors of 10298 and 10304.

Prime Factorization of 10298

Prime factors of 10298 are 2, 19, 271. Prime factorization of 10298 in exponential form is:

10298 = 21 × 191 × 2711

Prime Factorization of 10304

Prime factors of 10304 are 2, 7, 23. Prime factorization of 10304 in exponential form is:

10304 = 26 × 71 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 10298 and 10304.

LCM(10298,10304) = 26 × 191 × 2711 × 71 × 231
LCM(10298,10304) = 53055296