The ratio of two numbers are 3 : 4 and their L.C.M. is 84, then which number is greater number of the following?

Question

Accepted Answer

To determine which number is the greater number when the ratio of two numbers is 3:4 and their L.C.M. is 84, we need to follow these steps:

1. **Understanding the Ratio**: The ratio 3:4 means that if the first number is 3x, the second number is 4x, where x is a common multiplier.

2. **Calculating the Numbers**: 
   - The two numbers can be expressed as 3x and 4x.
   - The L.C.M. of these two numbers is given as 84.

3. **Finding the Value of x**:
   - The L.C.M. of 3x and 4x is calculated as the L.C.M. of 3 and 4 multiplied by x.
   - The L.C.M. of 3 and 4 is 12.
   - Therefore, 12x = 84.

4. **Solving for x**:
   - Divide both sides by 12 to find x: 
     $$
     x = \frac{84}{12} = 7
     $$

5. **Calculating the Actual Numbers**:
   - Substitute x = 7 back into the expressions for the numbers:
     - First number = 3x = 3 * 7 = 21
     - Second number = 4x = 4 * 7 = 28

6. **Identifying the Greater Number**:
   - Between 21 and 28, the greater number is 28.

7. **Explanation of Options**:
   - **Option 1 (21)**: This is the smaller number in the ratio, not the greater one.
   - **Option 2 (24)**: This number does not fit the ratio 3:4 when the L.C.M. is 84.
   - **Option 3 (28)**: This is the correct answer as it is the greater number derived from the ratio 3:4 with the given L.C.M. of 84.
   - **Option 4 (84)**: This is the L.C.M. of the numbers, not one of the numbers themselves.

Therefore, the correct answer is Option 3, which is 28, as it is the greater number when the ratio is 3:4 and the L.C.M. is 84.