Question

the L.C.M of two numbers is 630 and their H.C.F is 9. If the sum of the numbers is 153, the difference is​

Answer 1

The difference between the two numbers whose LCM is 630 and HCF is 9, and the sum is 153, is 27.

Step-by-step explanation:

The Least Common Multiple (LCM) and Highest Common Factor (HCF) relationship is given by the formula:

LCM of two numbers × HCF of two numbers = Product of the two numbers

Given that LCM = 630 and HCF = 9, we can find the product of the two numbers as follows:

Product = LCM × HCF = 630 × 9 = 5670

Let the two numbers be x and y. Since the sum of the numbers is 153, we have:

x + y = 153

Now, we also know that the product of the two numbers (x × y) is 5670.

Using the system of equations:

• x + y = 153
• x × y = 5670

We can find the individual numbers x and y. Without loss of generality, we can solve the equations for x:

Solving for y from the first equation gives us y = 153 - x. Substituting y into the second equation:

x × (153 - x) = 5670

Expanding and solving the quadratic equation, we find that the two numbers are 90 and 63. Thus, the difference between the two numbers is:

90 - 63 = 27