What is the Least Common Multiple of 516 and 520?
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 516 and 520 is 67080.
LCM(516,520) = 67080
Least Common Multiple of 516 and 520 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 516 and 520, than apply into the LCM equation.
GCF(516,520) = 4
LCM(516,520) = ( 516 × 520) / 4
LCM(516,520) = 268320 / 4
LCM(516,520) = 67080
Least Common Multiple (LCM) of 516 and 520 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 516 and 520. First we will calculate the prime factors of 516 and 520.
Prime Factorization of 516
Prime factors of 516 are 2, 3, 43. Prime factorization of 516 in exponential form is:
516 = 22 × 31 × 431
Prime Factorization of 520
Prime factors of 520 are 2, 5, 13. Prime factorization of 520 in exponential form is:
520 = 23 × 51 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 516 and 520.
LCM(516,520) = 23 × 31 × 431 × 51 × 131
LCM(516,520) = 67080
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