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What is the Least Common Multiple of 67260 and 67270?

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 67260 and 67270 is 452458020.

LCM(67260,67270) = 452458020

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Least Common Multiple of 67260 and 67270 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67260 and 67270, than apply into the LCM equation.

GCF(67260,67270) = 10
LCM(67260,67270) = ( 67260 × 67270) / 10
LCM(67260,67270) = 4524580200 / 10
LCM(67260,67270) = 452458020

Least Common Multiple (LCM) of 67260 and 67270 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67260 and 67270. First we will calculate the prime factors of 67260 and 67270.

Prime Factorization of 67260

Prime factors of 67260 are 2, 3, 5, 19, 59. Prime factorization of 67260 in exponential form is:

67260 = 22 × 31 × 51 × 191 × 591

Prime Factorization of 67270

Prime factors of 67270 are 2, 5, 7, 31. Prime factorization of 67270 in exponential form is:

67270 = 21 × 51 × 71 × 312

Now multiplying the highest exponent prime factors to calculate the LCM of 67260 and 67270.

LCM(67260,67270) = 22 × 31 × 51 × 191 × 591 × 71 × 312
LCM(67260,67270) = 452458020