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What is the Least Common Multiple of 65714 and 65734?

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 65714 and 65734 is 2159822038.

LCM(65714,65734) = 2159822038

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Least Common Multiple of 65714 and 65734 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65714 and 65734, than apply into the LCM equation.

GCF(65714,65734) = 2
LCM(65714,65734) = ( 65714 × 65734) / 2
LCM(65714,65734) = 4319644076 / 2
LCM(65714,65734) = 2159822038

Least Common Multiple (LCM) of 65714 and 65734 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65714 and 65734. First we will calculate the prime factors of 65714 and 65734.

Prime Factorization of 65714

Prime factors of 65714 are 2, 11, 29, 103. Prime factorization of 65714 in exponential form is:

65714 = 21 × 111 × 291 × 1031

Prime Factorization of 65734

Prime factors of 65734 are 2, 23, 1429. Prime factorization of 65734 in exponential form is:

65734 = 21 × 231 × 14291

Now multiplying the highest exponent prime factors to calculate the LCM of 65714 and 65734.

LCM(65714,65734) = 21 × 111 × 291 × 1031 × 231 × 14291
LCM(65714,65734) = 2159822038