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What is the Least Common Multiple of 10530 and 10538?

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 10530 and 10538 is 55482570.

LCM(10530,10538) = 55482570

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Least Common Multiple of 10530 and 10538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10530 and 10538, than apply into the LCM equation.

GCF(10530,10538) = 2
LCM(10530,10538) = ( 10530 × 10538) / 2
LCM(10530,10538) = 110965140 / 2
LCM(10530,10538) = 55482570

Least Common Multiple (LCM) of 10530 and 10538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10530 and 10538. First we will calculate the prime factors of 10530 and 10538.

Prime Factorization of 10530

Prime factors of 10530 are 2, 3, 5, 13. Prime factorization of 10530 in exponential form is:

10530 = 21 × 34 × 51 × 131

Prime Factorization of 10538

Prime factors of 10538 are 2, 11, 479. Prime factorization of 10538 in exponential form is:

10538 = 21 × 111 × 4791

Now multiplying the highest exponent prime factors to calculate the LCM of 10530 and 10538.

LCM(10530,10538) = 21 × 34 × 51 × 131 × 111 × 4791
LCM(10530,10538) = 55482570