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What is the Least Common Multiple of 67496 and 67509?

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 67496 and 67509 is 350506728.

LCM(67496,67509) = 350506728

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Least Common Multiple of 67496 and 67509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67496 and 67509, than apply into the LCM equation.

GCF(67496,67509) = 13
LCM(67496,67509) = ( 67496 × 67509) / 13
LCM(67496,67509) = 4556587464 / 13
LCM(67496,67509) = 350506728

Least Common Multiple (LCM) of 67496 and 67509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67496 and 67509. First we will calculate the prime factors of 67496 and 67509.

Prime Factorization of 67496

Prime factors of 67496 are 2, 11, 13, 59. Prime factorization of 67496 in exponential form is:

67496 = 23 × 111 × 131 × 591

Prime Factorization of 67509

Prime factors of 67509 are 3, 13, 577. Prime factorization of 67509 in exponential form is:

67509 = 32 × 131 × 5771

Now multiplying the highest exponent prime factors to calculate the LCM of 67496 and 67509.

LCM(67496,67509) = 23 × 111 × 131 × 591 × 32 × 5771
LCM(67496,67509) = 350506728