What is the Least Common Multiple of 15 and 20?
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 15 and 20 is 60.
LCM(15,20) = 60
Least Common Multiple of 15 and 20 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 20, than apply into the LCM equation.
GCF(15,20) = 5
LCM(15,20) = ( 15 × 20) / 5
LCM(15,20) = 300 / 5
LCM(15,20) = 60
Least Common Multiple (LCM) of 15 and 20 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 20. First we will calculate the prime factors of 15 and 20.
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
Prime Factorization of 20
Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:
20 = 22 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 20.
LCM(15,20) = 31 × 51 × 22
LCM(15,20) = 60