What is the Least Common Multiple of 21459 and 21465?
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 21459 and 21465 is 153539145.
LCM(21459,21465) = 153539145
Least Common Multiple of 21459 and 21465 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21459 and 21465, than apply into the LCM equation.
GCF(21459,21465) = 3
LCM(21459,21465) = ( 21459 × 21465) / 3
LCM(21459,21465) = 460617435 / 3
LCM(21459,21465) = 153539145
Least Common Multiple (LCM) of 21459 and 21465 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21459 and 21465. First we will calculate the prime factors of 21459 and 21465.
Prime Factorization of 21459
Prime factors of 21459 are 3, 23, 311. Prime factorization of 21459 in exponential form is:
21459 = 31 × 231 × 3111
Prime Factorization of 21465
Prime factors of 21465 are 3, 5, 53. Prime factorization of 21465 in exponential form is:
21465 = 34 × 51 × 531
Now multiplying the highest exponent prime factors to calculate the LCM of 21459 and 21465.
LCM(21459,21465) = 34 × 231 × 3111 × 51 × 531
LCM(21459,21465) = 153539145
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