What is the Least Common Multiple of 5 and 6?
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 5 and 6 is 30.
LCM(5,6) = 30
Least Common Multiple of 5 and 6 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 6, than apply into the LCM equation.
GCF(5,6) = 1
LCM(5,6) = ( 5 × 6) / 1
LCM(5,6) = 30 / 1
LCM(5,6) = 30
Least Common Multiple (LCM) of 5 and 6 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 6. First we will calculate the prime factors of 5 and 6.
Prime Factorization of 5
Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:
5 = 51
Prime Factorization of 6
Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:
6 = 21 × 31
Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 6.
LCM(5,6) = 51 × 21 × 31
LCM(5,6) = 30