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What is the Least Common Multiple of 67494 and 67512?

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 67494 and 67512 is 759442488.

LCM(67494,67512) = 759442488

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Least Common Multiple of 67494 and 67512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67494 and 67512, than apply into the LCM equation.

GCF(67494,67512) = 6
LCM(67494,67512) = ( 67494 × 67512) / 6
LCM(67494,67512) = 4556654928 / 6
LCM(67494,67512) = 759442488

Least Common Multiple (LCM) of 67494 and 67512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67494 and 67512. First we will calculate the prime factors of 67494 and 67512.

Prime Factorization of 67494

Prime factors of 67494 are 2, 3, 7, 1607. Prime factorization of 67494 in exponential form is:

67494 = 21 × 31 × 71 × 16071

Prime Factorization of 67512

Prime factors of 67512 are 2, 3, 29, 97. Prime factorization of 67512 in exponential form is:

67512 = 23 × 31 × 291 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 67494 and 67512.

LCM(67494,67512) = 23 × 31 × 71 × 16071 × 291 × 971
LCM(67494,67512) = 759442488