Three numbers are in the ratio of 3: 4: 5 and their
L.C.M. is 2400. Their H.C.F. is

Question

Accepted Answer

**LCM Calculation:**
   The LCM of these numbers is given as $$2400$$. The LCM of $$3x$$, $$4x$$, and $$5x$$ can also be expressed as $$60x$$ (since the LCM of 3, 4, and 5 is 60). Equating this to the given LCM:
   $$
   60x = 2400
   $$
   Solving for $$x$$:
   $$
   x = \frac{2400}{60} = 40
   $$

**Finding the Numbers:**
   Substituting $$x = 40$$ into the expressions for the numbers:
   - First number: $$3 	imes 40 = 120$$
   - Second number: $$4 	imes 40 = 160$$
   - Third number: $$5 	imes 40 = 200$$

Thus, the numbers are $$120, 160, 	ext{and } 200$$.

**HCF Calculation:**
   The HCF of these numbers is equal to the value of $$x$$, since $$x$$ represents the greatest common divisor that divides all three numbers. Therefore:
   $$
   	ext{HCF} = x = 40
   $$

**Final Answer:** The required HCF is **40**.

Answer

Answer

Answer