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What is the Least Common Multiple of 10710 and 10714?

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 10710 and 10714 is 57373470.

LCM(10710,10714) = 57373470

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Least Common Multiple of 10710 and 10714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10710 and 10714, than apply into the LCM equation.

GCF(10710,10714) = 2
LCM(10710,10714) = ( 10710 × 10714) / 2
LCM(10710,10714) = 114746940 / 2
LCM(10710,10714) = 57373470

Least Common Multiple (LCM) of 10710 and 10714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10710 and 10714. First we will calculate the prime factors of 10710 and 10714.

Prime Factorization of 10710

Prime factors of 10710 are 2, 3, 5, 7, 17. Prime factorization of 10710 in exponential form is:

10710 = 21 × 32 × 51 × 71 × 171

Prime Factorization of 10714

Prime factors of 10714 are 2, 11, 487. Prime factorization of 10714 in exponential form is:

10714 = 21 × 111 × 4871

Now multiplying the highest exponent prime factors to calculate the LCM of 10710 and 10714.

LCM(10710,10714) = 21 × 32 × 51 × 71 × 171 × 111 × 4871
LCM(10710,10714) = 57373470