Sure, let's go through the solution step by step.
To solve the problem, we'll use the relationship between the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of two numbers:
[tex]\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \][/tex]
Given:
- [tex]\(\text{HCF}(2520, 6600) = 1\)[/tex]
- [tex]\(\text{LCM}(2520, 6600) = 252 \times 10^3\)[/tex]
We are required to find the value of [tex]\(k'\)[/tex].
The provided relationship for HCF and LCM tells us:
[tex]\[ 1 \times (252 \times 10^3) = 2520 \times 6600 \][/tex]
We need to determine the value corresponding to [tex]\(k'\)[/tex]. Given the structure in the question, [tex]\(k'\)[/tex] refers to the value connected with the LCM provided.
Since the LCM given is [tex]\(252 \times 10^3\)[/tex], we recognize that the LCM is indeed [tex]\(252000\)[/tex].
So, the value of [tex]\(k'\)[/tex] is:
[tex]\[
k' = 252000
\][/tex]
Thus, we can express [tex]\(k'\)[/tex] in another form, dividing by [tex]\(1000\)[/tex]:
[tex]\[
\frac{LCM}{1000} = \frac{252000}{1000} = 252.0
\][/tex]
Thus, the solution is:
[tex]\[
k = 252000
\][/tex]
and
[tex]\[
\frac{LCM}{1000} = 252.0
\][/tex]
Therefore,:
[tex]\[ k' = \boxed{252000} \][/tex]
