What is the Least Common Multiple of 30 and 48?
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 30 and 48 is 240.
LCM(30,48) = 240
Least Common Multiple of 30 and 48 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 48, than apply into the LCM equation.
GCF(30,48) = 6
LCM(30,48) = ( 30 × 48) / 6
LCM(30,48) = 1440 / 6
LCM(30,48) = 240
Least Common Multiple (LCM) of 30 and 48 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 48. First we will calculate the prime factors of 30 and 48.
Prime Factorization of 30
Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:
30 = 21 × 31 × 51
Prime Factorization of 48
Prime factors of 48 are 2, 3. Prime factorization of 48 in exponential form is:
48 = 24 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 48.
LCM(30,48) = 24 × 31 × 51
LCM(30,48) = 240