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What is the Least Common Multiple of 822 and 834?

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 822 and 834 is 114258.

LCM(822,834) = 114258

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Least Common Multiple of 822 and 834 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 822 and 834, than apply into the LCM equation.

GCF(822,834) = 6
LCM(822,834) = ( 822 × 834) / 6
LCM(822,834) = 685548 / 6
LCM(822,834) = 114258

Least Common Multiple (LCM) of 822 and 834 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 822 and 834. First we will calculate the prime factors of 822 and 834.

Prime Factorization of 822

Prime factors of 822 are 2, 3, 137. Prime factorization of 822 in exponential form is:

822 = 21 × 31 × 1371

Prime Factorization of 834

Prime factors of 834 are 2, 3, 139. Prime factorization of 834 in exponential form is:

834 = 21 × 31 × 1391

Now multiplying the highest exponent prime factors to calculate the LCM of 822 and 834.

LCM(822,834) = 21 × 31 × 1371 × 1391
LCM(822,834) = 114258