What is the Least Common Multiple of 18720 and 18740?
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 18720 and 18740 is 17540640.
LCM(18720,18740) = 17540640
Least Common Multiple of 18720 and 18740 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 18720 and 18740, than apply into the LCM equation.
GCF(18720,18740) = 20
LCM(18720,18740) = ( 18720 × 18740) / 20
LCM(18720,18740) = 350812800 / 20
LCM(18720,18740) = 17540640
Least Common Multiple (LCM) of 18720 and 18740 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 18720 and 18740. First we will calculate the prime factors of 18720 and 18740.
Prime Factorization of 18720
Prime factors of 18720 are 2, 3, 5, 13. Prime factorization of 18720 in exponential form is:
18720 = 25 × 32 × 51 × 131
Prime Factorization of 18740
Prime factors of 18740 are 2, 5, 937. Prime factorization of 18740 in exponential form is:
18740 = 22 × 51 × 9371
Now multiplying the highest exponent prime factors to calculate the LCM of 18720 and 18740.
LCM(18720,18740) = 25 × 32 × 51 × 131 × 9371
LCM(18720,18740) = 17540640
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