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What is the Least Common Multiple of 10406 and 10416?

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 10406 and 10416 is 54194448.

LCM(10406,10416) = 54194448

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Least Common Multiple of 10406 and 10416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10406 and 10416, than apply into the LCM equation.

GCF(10406,10416) = 2
LCM(10406,10416) = ( 10406 × 10416) / 2
LCM(10406,10416) = 108388896 / 2
LCM(10406,10416) = 54194448

Least Common Multiple (LCM) of 10406 and 10416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10406 and 10416. First we will calculate the prime factors of 10406 and 10416.

Prime Factorization of 10406

Prime factors of 10406 are 2, 11, 43. Prime factorization of 10406 in exponential form is:

10406 = 21 × 112 × 431

Prime Factorization of 10416

Prime factors of 10416 are 2, 3, 7, 31. Prime factorization of 10416 in exponential form is:

10416 = 24 × 31 × 71 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 10406 and 10416.

LCM(10406,10416) = 24 × 112 × 431 × 31 × 71 × 311
LCM(10406,10416) = 54194448