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What is the Least Common Multiple of 8498 and 8514?

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 8498 and 8514 is 36175986.

LCM(8498,8514) = 36175986

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Least Common Multiple of 8498 and 8514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8498 and 8514, than apply into the LCM equation.

GCF(8498,8514) = 2
LCM(8498,8514) = ( 8498 × 8514) / 2
LCM(8498,8514) = 72351972 / 2
LCM(8498,8514) = 36175986

Least Common Multiple (LCM) of 8498 and 8514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8498 and 8514. First we will calculate the prime factors of 8498 and 8514.

Prime Factorization of 8498

Prime factors of 8498 are 2, 7, 607. Prime factorization of 8498 in exponential form is:

8498 = 21 × 71 × 6071

Prime Factorization of 8514

Prime factors of 8514 are 2, 3, 11, 43. Prime factorization of 8514 in exponential form is:

8514 = 21 × 32 × 111 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 8498 and 8514.

LCM(8498,8514) = 21 × 71 × 6071 × 32 × 111 × 431
LCM(8498,8514) = 36175986