Alright, let's solve this step-by-step.
Given:
- The highest common factor (HCF) of the two numbers is 9.
- The least common multiple (LCM) of the two numbers is 459.
- One of the numbers is 27.
- We need to find the other number.
We can use the relationship between HCF, LCM, and the product of two numbers, which is:
[tex]\[
\text{HCF} \times \text{LCM} = \text{Product of the two numbers}
\][/tex]
Let [tex]\(a\)[/tex] and [tex]\(b\)[/tex] be the two numbers. Given:
- [tex]\(a = 27\)[/tex]
- [tex]\(\text{HCF}(a, b) = 9\)[/tex]
- [tex]\(\text{LCM}(a, b) = 459\)[/tex]
From the relationship, we have:
[tex]\[
\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b
\][/tex]
Substitute the known values:
[tex]\[
9 \times 459 = 27 \times b
\][/tex]
We need to solve for [tex]\(b\)[/tex].
[tex]\[
27 \times b = 9 \times 459
\][/tex]
First, calculate the right-hand side:
[tex]\[
9 \times 459 = 4131
\][/tex]
So the equation becomes:
[tex]\[
27 \times b = 4131
\][/tex]
Now, solve for [tex]\(b\)[/tex]:
[tex]\[
b = \frac{4131}{27}
\][/tex]
Perform the division:
[tex]\[
b = 153
\][/tex]
Therefore, the other number is [tex]\(153\)[/tex].
