What is the Least Common Multiple of 4 and 30?
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 4 and 30 is 60.
LCM(4,30) = 60
Least Common Multiple of 4 and 30 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4 and 30, than apply into the LCM equation.
GCF(4,30) = 2
LCM(4,30) = ( 4 × 30) / 2
LCM(4,30) = 120 / 2
LCM(4,30) = 60
Least Common Multiple (LCM) of 4 and 30 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 4 and 30. First we will calculate the prime factors of 4 and 30.
Prime Factorization of 4
Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:
4 = 22
Prime Factorization of 30
Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:
30 = 21 × 31 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 4 and 30.
LCM(4,30) = 22 × 31 × 51
LCM(4,30) = 60