Question

The ratio of two numbers is 3 : 5 and their LCM is 42 greater than their HCF. What is the value of the larger number?

1. 18
2. 12
3. 15
4. 9

Answer 1

To find the value of the larger number, we need to first understand the concept of the LCM (Least Common Multiple) and HCF (Highest Common Factor). The LCM is the smallest multiple that two numbers have in common, while the HCF is the largest factor that two numbers have in common. In this case, the question is invalid.

Step-by-step explanation:

To find the value of the larger number, we need to first understand the concept of the LCM (Least Common Multiple) and HCF (Highest Common Factor). The LCM is the smallest multiple that two numbers have in common, while the HCF is the largest factor that two numbers have in common. In this case, let the numbers be 3x and 5x, where x is a constant. The LCM of 3x and 5x is 42 greater than their HCF, which means LCM is 42 + HCF.

We can write the equation: LCM = HCF + 42

We also know that the LCM of 3 and 5 is 15, so: LCM = 15

Substituting the values, we get: 15 = HCF + 42

Simplifying, we find: HCF = -27

Since HCF represents a factor, it cannot be negative. Therefore, there is no solution. The question is Invalid.