Question

The LCM of two numbers is 72. Their ratio is 3 : 4. Find the sum of the numbers.

• A. 38
• B. 40
• C. 44
• D. 42

Answer 1

Answer:

D. 42

The sum of the two numbers is 42

1. Find the ratio parts:

   • The numbers are in the ratio 3 : 4.

   • Let the numbers be 3x and 4x

2. Find the LCM of the ratios:

   • The LCM of the ratio parts 3 and 4 is 12.

   • Therefore, the LCM of 3x and 4x is 12x

3. Solve for x

   • Given that LCM = 72, we can set up the equation:
     $12x=72$
     $x=\frac{72}{12}=6$

4. Calculate the sum:

   • The sum of the ratios is 3 + 4 = 7 parts.

   • Total Sum = $7x = 7 \times 6 = 42$