The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is:

Options

A. 50
B. 75
C. 65
D. 100

Answer

To find the other number when given the HCF, LCM, and one of the numbers, we can use the relationship between these values. Here’s how to solve the problem step by step:

### Step 1: Understand the relationship
We know that the product of the HCF (also known as GCD) and LCM of two numbers is equal to the product of the two numbers. This can be expressed as:
\[ \text{HCF} \times \text{LCM} = n_1 \times n_2 \]
where \( n_1 \) and \( n_2 \) are the two numbers.

### Step 2: Substitute the known values
From the question, we have:
- HCF = 15
- LCM = 300
- One number \( n_1 = 60 \)
- The other number \( n_2 = x \) (which we need to find)

Substituting these values into the equation gives us:
\[ 15 \times 300 = 60 \times x \]

### Step 3: Calculate the left side
Now, calculate the left side:
\[ 15 \times 300 = 4500 \]

### Step 4: Set up the equation
Now we can set up the equation:
\[ 4500 = 60 \times x \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 60:
\[ x = \frac{4500}{60} \]

### Step 6: Simplify the division
Now, simplify \( \frac{4500}{60} \):
- First, we can cancel out a zero from both the numerator and the denominator:
\[ x = \frac{450}{6} \]

- Now perform the division:
\[ x = 75 \]

### Conclusion
Thus, the other number is:
\[ x = 75 \]