Question

The ratio between two numbers is 4:5. Their LCM is 120 , the sum of numbers is :

• A. 30
• B. 24
• C. 54
• D. 44

Answer 1

Answer:

C. 54

The sum of the numbers is 54.

1. Find the common multiplier ($x$):
   Let the two numbers be $4x$ and $5x$.
   Since 4 and 5 are co-prime (they share no common factors other than 1), their LCM will be:
   $\text{LCM} = 4 \times 5 \times x = 20x$

2. Solve for $x$:
   Given that the LCM is 120:
   $20x = 120$
   $x = \frac{120}{20} = 6$

3. Find the numbers:

   • First number $= 4 \times 6 = \mathbf{24}$

   • Second number $= 5 \times 6 = \mathbf{30}$

4. Calculate the sum:
   $\text{Sum} = 24 + 30 = \mathbf{54}$