Finding the Other Number Using HCF and LCM

To solve this problem, we use the fundamental relationship between two numbers and their Highest Common Factor (H.C.F.) and Least Common Multiple (L.C.M.). The relationship is stated as:

Product of the two numbers = H.C.F. × L.C.M.

Let the two numbers be $Number1$ and $Number2$. We are given:

• H.C.F. = 5
• L.C.M. = 495
• $Number1$ = 55
• We need to find $Number2$.

Applying the HCF-LCM Formula

Using the formula:

$ \text{Number1} \times \text{Number2} = \text{H.C.F.} \times \text{L.C.M.} $

Substitute the given values into the equation:

$ 55 \times \text{Number2} = 5 \times 495 $

Calculating the Other Number

First, calculate the product of the H.C.F. and L.C.M.:

$ 5 \times 495 = 2475 $

Now, the equation becomes:

$ 55 \times \text{Number2} = 2475 $

To find $Number2$, divide the product by the known number (55):

$ \text{Number2} = \frac{2475}{55} $

Performing the division:

$ \text{Number2} = 45 $

Therefore, the other number is 45.