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What is the Least Common Multiple of 67512 and 67530?

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 67512 and 67530 is 759847560.

LCM(67512,67530) = 759847560

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Least Common Multiple of 67512 and 67530 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67512 and 67530, than apply into the LCM equation.

GCF(67512,67530) = 6
LCM(67512,67530) = ( 67512 × 67530) / 6
LCM(67512,67530) = 4559085360 / 6
LCM(67512,67530) = 759847560

Least Common Multiple (LCM) of 67512 and 67530 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67512 and 67530. First we will calculate the prime factors of 67512 and 67530.

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

Prime Factorization of 67530

Prime factors of 67530 are 2, 3, 5, 2251. Prime factorization of 67530 in exponential form is:

67530 = 21 × 31 × 51 × 22511

Now multiplying the highest exponent prime factors to calculate the LCM of 67512 and 67530.

LCM(67512,67530) = 23 × 31 × 291 × 971 × 51 × 22511
LCM(67512,67530) = 759847560