What is the Least Common Multiple of 13506 and 13512?
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 13506 and 13512 is 30415512.
LCM(13506,13512) = 30415512
Least Common Multiple of 13506 and 13512 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13506 and 13512, than apply into the LCM equation.
GCF(13506,13512) = 6
LCM(13506,13512) = ( 13506 × 13512) / 6
LCM(13506,13512) = 182493072 / 6
LCM(13506,13512) = 30415512
Least Common Multiple (LCM) of 13506 and 13512 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13506 and 13512. First we will calculate the prime factors of 13506 and 13512.
Prime Factorization of 13506
Prime factors of 13506 are 2, 3, 2251. Prime factorization of 13506 in exponential form is:
13506 = 21 × 31 × 22511
Prime Factorization of 13512
Prime factors of 13512 are 2, 3, 563. Prime factorization of 13512 in exponential form is:
13512 = 23 × 31 × 5631
Now multiplying the highest exponent prime factors to calculate the LCM of 13506 and 13512.
LCM(13506,13512) = 23 × 31 × 22511 × 5631
LCM(13506,13512) = 30415512
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