What is the Least Common Multiple of 20 and 24?
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 20 and 24 is 120.
LCM(20,24) = 120
Least Common Multiple of 20 and 24 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 24, than apply into the LCM equation.
GCF(20,24) = 4
LCM(20,24) = ( 20 × 24) / 4
LCM(20,24) = 480 / 4
LCM(20,24) = 120
Least Common Multiple (LCM) of 20 and 24 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 24. First we will calculate the prime factors of 20 and 24.
Prime Factorization of 20
Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:
20 = 22 × 51
Prime Factorization of 24
Prime factors of 24 are 2, 3. Prime factorization of 24 in exponential form is:
24 = 23 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 20 and 24.
LCM(20,24) = 23 × 51 × 31
LCM(20,24) = 120