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What is the Least Common Multiple of 67284 and 67298?

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 67284 and 67298 is 323434188.

LCM(67284,67298) = 323434188

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Least Common Multiple of 67284 and 67298 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67284 and 67298, than apply into the LCM equation.

GCF(67284,67298) = 14
LCM(67284,67298) = ( 67284 × 67298) / 14
LCM(67284,67298) = 4528078632 / 14
LCM(67284,67298) = 323434188

Least Common Multiple (LCM) of 67284 and 67298 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67284 and 67298. First we will calculate the prime factors of 67284 and 67298.

Prime Factorization of 67284

Prime factors of 67284 are 2, 3, 7, 89. Prime factorization of 67284 in exponential form is:

67284 = 22 × 33 × 71 × 891

Prime Factorization of 67298

Prime factors of 67298 are 2, 7, 11, 19, 23. Prime factorization of 67298 in exponential form is:

67298 = 21 × 71 × 111 × 191 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 67284 and 67298.

LCM(67284,67298) = 22 × 33 × 71 × 891 × 111 × 191 × 231
LCM(67284,67298) = 323434188