What is the Least Common Multiple of 20405 and 20424?
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 20405 and 20424 is 416751720.
LCM(20405,20424) = 416751720
Least Common Multiple of 20405 and 20424 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20405 and 20424, than apply into the LCM equation.
GCF(20405,20424) = 1
LCM(20405,20424) = ( 20405 × 20424) / 1
LCM(20405,20424) = 416751720 / 1
LCM(20405,20424) = 416751720
Least Common Multiple (LCM) of 20405 and 20424 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 20405 and 20424. First we will calculate the prime factors of 20405 and 20424.
Prime Factorization of 20405
Prime factors of 20405 are 5, 7, 11, 53. Prime factorization of 20405 in exponential form is:
20405 = 51 × 71 × 111 × 531
Prime Factorization of 20424
Prime factors of 20424 are 2, 3, 23, 37. Prime factorization of 20424 in exponential form is:
20424 = 23 × 31 × 231 × 371
Now multiplying the highest exponent prime factors to calculate the LCM of 20405 and 20424.
LCM(20405,20424) = 51 × 71 × 111 × 531 × 23 × 31 × 231 × 371
LCM(20405,20424) = 416751720
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