What is the Least Common Multiple of 20340 and 20352?
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 20340 and 20352 is 34496640.
LCM(20340,20352) = 34496640
Least Common Multiple of 20340 and 20352 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20340 and 20352, than apply into the LCM equation.
GCF(20340,20352) = 12
LCM(20340,20352) = ( 20340 × 20352) / 12
LCM(20340,20352) = 413959680 / 12
LCM(20340,20352) = 34496640
Least Common Multiple (LCM) of 20340 and 20352 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 20340 and 20352. First we will calculate the prime factors of 20340 and 20352.
Prime Factorization of 20340
Prime factors of 20340 are 2, 3, 5, 113. Prime factorization of 20340 in exponential form is:
20340 = 22 × 32 × 51 × 1131
Prime Factorization of 20352
Prime factors of 20352 are 2, 3, 53. Prime factorization of 20352 in exponential form is:
20352 = 27 × 31 × 531
Now multiplying the highest exponent prime factors to calculate the LCM of 20340 and 20352.
LCM(20340,20352) = 27 × 32 × 51 × 1131 × 531
LCM(20340,20352) = 34496640
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