What is the Least Common Multiple of 19830 and 19845?
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 19830 and 19845 is 26235090.
LCM(19830,19845) = 26235090
Least Common Multiple of 19830 and 19845 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19830 and 19845, than apply into the LCM equation.
GCF(19830,19845) = 15
LCM(19830,19845) = ( 19830 × 19845) / 15
LCM(19830,19845) = 393526350 / 15
LCM(19830,19845) = 26235090
Least Common Multiple (LCM) of 19830 and 19845 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 19830 and 19845. First we will calculate the prime factors of 19830 and 19845.
Prime Factorization of 19830
Prime factors of 19830 are 2, 3, 5, 661. Prime factorization of 19830 in exponential form is:
19830 = 21 × 31 × 51 × 6611
Prime Factorization of 19845
Prime factors of 19845 are 3, 5, 7. Prime factorization of 19845 in exponential form is:
19845 = 34 × 51 × 72
Now multiplying the highest exponent prime factors to calculate the LCM of 19830 and 19845.
LCM(19830,19845) = 21 × 34 × 51 × 6611 × 72
LCM(19830,19845) = 26235090
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