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What is the Least Common Multiple of 509 and 525?

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 509 and 525 is 267225.

LCM(509,525) = 267225

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Least Common Multiple of 509 and 525 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 509 and 525, than apply into the LCM equation.

GCF(509,525) = 1
LCM(509,525) = ( 509 × 525) / 1
LCM(509,525) = 267225 / 1
LCM(509,525) = 267225

Least Common Multiple (LCM) of 509 and 525 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 509 and 525. First we will calculate the prime factors of 509 and 525.

Prime Factorization of 509

Prime factors of 509 are 509. Prime factorization of 509 in exponential form is:

509 = 5091

Prime Factorization of 525

Prime factors of 525 are 3, 5, 7. Prime factorization of 525 in exponential form is:

525 = 31 × 52 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 509 and 525.

LCM(509,525) = 5091 × 31 × 52 × 71
LCM(509,525) = 267225