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What is the Least Common Multiple of 9814 and 9824?

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 9814 and 9824 is 48206368.

LCM(9814,9824) = 48206368

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Least Common Multiple of 9814 and 9824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9814 and 9824, than apply into the LCM equation.

GCF(9814,9824) = 2
LCM(9814,9824) = ( 9814 × 9824) / 2
LCM(9814,9824) = 96412736 / 2
LCM(9814,9824) = 48206368

Least Common Multiple (LCM) of 9814 and 9824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9814 and 9824. First we will calculate the prime factors of 9814 and 9824.

Prime Factorization of 9814

Prime factors of 9814 are 2, 7, 701. Prime factorization of 9814 in exponential form is:

9814 = 21 × 71 × 7011

Prime Factorization of 9824

Prime factors of 9824 are 2, 307. Prime factorization of 9824 in exponential form is:

9824 = 25 × 3071

Now multiplying the highest exponent prime factors to calculate the LCM of 9814 and 9824.

LCM(9814,9824) = 25 × 71 × 7011 × 3071
LCM(9814,9824) = 48206368