What is the Least Common Multiple of 30504 and 30514?
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 30504 and 30514 is 465399528.
LCM(30504,30514) = 465399528
Least Common Multiple of 30504 and 30514 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30504 and 30514, than apply into the LCM equation.
GCF(30504,30514) = 2
LCM(30504,30514) = ( 30504 × 30514) / 2
LCM(30504,30514) = 930799056 / 2
LCM(30504,30514) = 465399528
Least Common Multiple (LCM) of 30504 and 30514 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30504 and 30514. First we will calculate the prime factors of 30504 and 30514.
Prime Factorization of 30504
Prime factors of 30504 are 2, 3, 31, 41. Prime factorization of 30504 in exponential form is:
30504 = 23 × 31 × 311 × 411
Prime Factorization of 30514
Prime factors of 30514 are 2, 11, 19, 73. Prime factorization of 30514 in exponential form is:
30514 = 21 × 111 × 191 × 731
Now multiplying the highest exponent prime factors to calculate the LCM of 30504 and 30514.
LCM(30504,30514) = 23 × 31 × 311 × 411 × 111 × 191 × 731
LCM(30504,30514) = 465399528
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