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What is the Least Common Multiple of 803 and 822?

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 803 and 822 is 660066.

LCM(803,822) = 660066

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Least Common Multiple of 803 and 822 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 803 and 822, than apply into the LCM equation.

GCF(803,822) = 1
LCM(803,822) = ( 803 × 822) / 1
LCM(803,822) = 660066 / 1
LCM(803,822) = 660066

Least Common Multiple (LCM) of 803 and 822 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 803 and 822. First we will calculate the prime factors of 803 and 822.

Prime Factorization of 803

Prime factors of 803 are 11, 73. Prime factorization of 803 in exponential form is:

803 = 111 × 731

Prime Factorization of 822

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

822 = 21 × 31 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 803 and 822.

LCM(803,822) = 111 × 731 × 21 × 31 × 1371
LCM(803,822) = 660066