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What is the Least Common Multiple of 67298 and 67310?

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 67298 and 67310 is 2264914190.

LCM(67298,67310) = 2264914190

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Least Common Multiple of 67298 and 67310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67298 and 67310, than apply into the LCM equation.

GCF(67298,67310) = 2
LCM(67298,67310) = ( 67298 × 67310) / 2
LCM(67298,67310) = 4529828380 / 2
LCM(67298,67310) = 2264914190

Least Common Multiple (LCM) of 67298 and 67310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67298 and 67310. First we will calculate the prime factors of 67298 and 67310.

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

Prime Factorization of 67310

Prime factors of 67310 are 2, 5, 53, 127. Prime factorization of 67310 in exponential form is:

67310 = 21 × 51 × 531 × 1271

Now multiplying the highest exponent prime factors to calculate the LCM of 67298 and 67310.

LCM(67298,67310) = 21 × 71 × 111 × 191 × 231 × 51 × 531 × 1271
LCM(67298,67310) = 2264914190