If the product of two numbers is 1050 and their HCF is 25, find their LCM.

Answer

To find the LCM of two numbers when their product and HCF are given, we can use the relationship between the product of the numbers, their HCF, and their LCM. Here’s the step-by-step solution:

**Step 1: Write down the relationship between HCF, LCM, and the product of the numbers.**
The relationship is given by the formula:
\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]

**Step 2: Substitute the known values into the formula.**
We know the product of the two numbers is 1050 and the HCF is 25. Therefore, we can write:
\[ 1050 = 25 \times \text{LCM} \]

**Step 3: Solve for LCM.**
To find the LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{1050}{25} \]

**Step 4: Perform the division.**
Now, we calculate:
\[ \text{LCM} = \frac{1050}{25} = 42 \]

Thus, the LCM of the two numbers is **42**.