Answer:
LCM (k, n) = 10 and HCF(k, n) = 2
Step-by-step explanation:
The given parameters are;
The time after which Keshav takes a break = k hours
The value of k = The first smallest prime natural number
Therefore, by mathematical definition, k = 2
The time after which Noel takes a break = n hours
The value of n = The fifth smallest composite natural number
The first five composite numbers are given as follows;
4, 6, 8, 9, and 10
Therefore, the fifth smallest composite natural number = 10 = n
The LCM (k, n) = LCM (2, 10) = Least common multiple of 2 and 10 is given as follows;
Dividing by 2, we get;
2/2 = 1, 10/2 = 5
Dividing the result by 5, we get;
5/5 = 1
Multiplying the devisors together gives;
5 × 2 = 10
Therefore, the LCM of 2 and 10 = 10
LCM(2, 10) = LCM (k, n) = 10
The HCF(k, n) = HCF of 2 and 10 = The highest common factor that divides both 2 and 10 is given as follows;
Dividing 2 and 10 by 2 gives;
2/2 = 1 and 10/2 = 5
Therefore, HCF(k, n) = The highest common factor of 2 and 10 = HCF(2, 10) = 2
