Question

What is the value of x if the LCM of x and 18 is 36, and the HCF of x and 18 is 6?

A) x = 54
B) x = 72
C) x = 12
D) x = 24

Answer 1

The value of x is found by using the relationship LCM(x, 18) × HCF(x, 18) = x × 18. Substituting the given LCM and HCF values and solving for x gives us a value of 12, which is option C.

Step-by-step explanation:

To find the value of x when the least common multiple (LCM) of x and 18 is 36, and the highest common factor (HCF) of x and 18 is 6, we can use the relationship between the LCM, HCF, and the two numbers involved:

LCM(x, 18) × HCF(x, 18) = x × 18

Substituting the given values gives us:

36 × 6 = x × 18

Dividing both sides by 18 to isolate x gives us:

36 × 6 / 18 = x

216 / 18 = x

x = 12

Therefore, the value of x is 12, which corresponds to option C) x = 12.