To solve this problem, we need to find the Least Common Multiple (LCM) of two numbers, given that their Highest Common Factor (HIF) is 4 and their product is 160. Here's a detailed, step-by-step way to find the answer.
1. Understanding the Relationship:
We know the relationship between the HIF, LCM, and the product of two numbers:
[tex]\[
\text{HIF} \times \text{LCM} = \text{Product of the two numbers}
\][/tex]
2. Given Values:
- The HIF (Highest Common Factor) of the two numbers is 4.
- The product of the two numbers is 160.
3. Setting Up the Equation:
Using the relationship mentioned above:
[tex]\[
4 \times \text{LCM} = 160
\][/tex]
4. Solving for LCM:
To find the LCM, we need to isolate LCM on one side of the equation:
[tex]\[
\text{LCM} = \frac{160}{4}
\][/tex]
5. Calculating the LCM:
Now, perform the division:
[tex]\[
\text{LCM} = 40
\][/tex]
Therefore, the Least Common Multiple (LCM) of the two numbers is [tex]\(\boxed{40}\)[/tex].
