What is the Least Common Multiple of 518 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 518 and 538 is 139342.
LCM(518,538) = 139342
Least Common Multiple of 518 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 518 and 538, than apply into the LCM equation.
GCF(518,538) = 2
LCM(518,538) = ( 518 × 538) / 2
LCM(518,538) = 278684 / 2
LCM(518,538) = 139342
Least Common Multiple (LCM) of 518 and 538 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 518 and 538. First we will calculate the prime factors of 518 and 538.
Prime Factorization of 518
Prime factors of 518 are 2, 7, 37. Prime factorization of 518 in exponential form is:
518 = 21 × 71 × 371
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 518 and 538.
LCM(518,538) = 21 × 71 × 371 × 2691
LCM(518,538) = 139342
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