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What is the Least Common Multiple of 67362 and 67382?

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 67362 and 67382 is 2269493142.

LCM(67362,67382) = 2269493142

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Least Common Multiple of 67362 and 67382 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67362 and 67382, than apply into the LCM equation.

GCF(67362,67382) = 2
LCM(67362,67382) = ( 67362 × 67382) / 2
LCM(67362,67382) = 4538986284 / 2
LCM(67362,67382) = 2269493142

Least Common Multiple (LCM) of 67362 and 67382 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67362 and 67382. First we will calculate the prime factors of 67362 and 67382.

Prime Factorization of 67362

Prime factors of 67362 are 2, 3, 103, 109. Prime factorization of 67362 in exponential form is:

67362 = 21 × 31 × 1031 × 1091

Prime Factorization of 67382

Prime factors of 67382 are 2, 7, 4813. Prime factorization of 67382 in exponential form is:

67382 = 21 × 71 × 48131

Now multiplying the highest exponent prime factors to calculate the LCM of 67362 and 67382.

LCM(67362,67382) = 21 × 31 × 1031 × 1091 × 71 × 48131
LCM(67362,67382) = 2269493142