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What is the Least Common Multiple of 10701 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 10701 and 10714 is 114650514.

LCM(10701,10714) = 114650514

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Least Common Multiple of 10701 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 10701 and 10714, than apply into the LCM equation.

GCF(10701,10714) = 1
LCM(10701,10714) = ( 10701 × 10714) / 1
LCM(10701,10714) = 114650514 / 1
LCM(10701,10714) = 114650514

Least Common Multiple (LCM) of 10701 and 10714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10701 and 10714. First we will calculate the prime factors of 10701 and 10714.

Prime Factorization of 10701

Prime factors of 10701 are 3, 29, 41. Prime factorization of 10701 in exponential form is:

10701 = 32 × 291 × 411

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 10701 and 10714.

LCM(10701,10714) = 32 × 291 × 411 × 21 × 111 × 4871
LCM(10701,10714) = 114650514