What is the Least Common Multiple of 19689 and 19700?
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 19689 and 19700 is 387873300.
LCM(19689,19700) = 387873300
Least Common Multiple of 19689 and 19700 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19689 and 19700, than apply into the LCM equation.
GCF(19689,19700) = 1
LCM(19689,19700) = ( 19689 × 19700) / 1
LCM(19689,19700) = 387873300 / 1
LCM(19689,19700) = 387873300
Least Common Multiple (LCM) of 19689 and 19700 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 19689 and 19700. First we will calculate the prime factors of 19689 and 19700.
Prime Factorization of 19689
Prime factors of 19689 are 3, 6563. Prime factorization of 19689 in exponential form is:
19689 = 31 × 65631
Prime Factorization of 19700
Prime factors of 19700 are 2, 5, 197. Prime factorization of 19700 in exponential form is:
19700 = 22 × 52 × 1971
Now multiplying the highest exponent prime factors to calculate the LCM of 19689 and 19700.
LCM(19689,19700) = 31 × 65631 × 22 × 52 × 1971
LCM(19689,19700) = 387873300
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