Question

Keshav and Noel started to cycle together from Nehru Park. Keshav takes a break to drink water after (k hours), where k is the first smallest prime natural number. Noel takes a break to drink water after (n hours), where n is the fifth smallest composite natural number.

Calculate the LCM (k, n) and HCF (k, n).

Answer 1

LCM (k, n) = 10 and HCF(k, n) = 2

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