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What is the Least Common Multiple of 520 and 538?

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 520 and 538 is 139880.

LCM(520,538) = 139880

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Least Common Multiple of 520 and 538 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 520 and 538, than apply into the LCM equation.

GCF(520,538) = 2
LCM(520,538) = ( 520 × 538) / 2
LCM(520,538) = 279760 / 2
LCM(520,538) = 139880

Least Common Multiple (LCM) of 520 and 538 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 520 and 538. First we will calculate the prime factors of 520 and 538.

Prime Factorization of 520

Prime factors of 520 are 2, 5, 13. Prime factorization of 520 in exponential form is:

520 = 23 × 51 × 131

Prime Factorization of 538

Prime factors of 538 are 2, 269. Prime factorization of 538 in exponential form is:

538 = 21 × 2691

Now multiplying the highest exponent prime factors to calculate the LCM of 520 and 538.

LCM(520,538) = 23 × 51 × 131 × 2691
LCM(520,538) = 139880