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What is the Least Common Multiple of 67821 and 67838?

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 67821 and 67838 is 4600840998.

LCM(67821,67838) = 4600840998

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Least Common Multiple of 67821 and 67838 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67821 and 67838, than apply into the LCM equation.

GCF(67821,67838) = 1
LCM(67821,67838) = ( 67821 × 67838) / 1
LCM(67821,67838) = 4600840998 / 1
LCM(67821,67838) = 4600840998

Least Common Multiple (LCM) of 67821 and 67838 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67821 and 67838. First we will calculate the prime factors of 67821 and 67838.

Prime Factorization of 67821

Prime factors of 67821 are 3, 13, 37, 47. Prime factorization of 67821 in exponential form is:

67821 = 31 × 131 × 371 × 471

Prime Factorization of 67838

Prime factors of 67838 are 2, 107, 317. Prime factorization of 67838 in exponential form is:

67838 = 21 × 1071 × 3171

Now multiplying the highest exponent prime factors to calculate the LCM of 67821 and 67838.

LCM(67821,67838) = 31 × 131 × 371 × 471 × 21 × 1071 × 3171
LCM(67821,67838) = 4600840998