The sum of LCM and HCF of two numbers is 854. If the LCM is 60 times the HCF and one of the numbers is 70, then the other number is:

Question

Accepted Answer

1. **Let the HCF be $$x$$:**  
   - Given that LCM is $$60x$$, the sum of HCF and LCM is:  
     $$
     x + 60x = 854.
     $$

2. **Solve for $$x$$:**  
   - Combine terms:  
     $$
     61x = 854 \implies x = \frac{854}{61} = 14.
     $$

3. **Determine HCF and LCM:**  
   - HCF = $$14$$, LCM = $$60 	imes 14 = 840$$.

4. **Find the other number using the relation between numbers, HCF, and LCM:**  
   - The product of two numbers equals the product of their HCF and LCM:  
     $$
     	ext{Number}_1 	imes 	ext{Number}_2 = HCF 	imes LCM.
     $$  
   - Substituting values:  
     $$
     70 	imes 	ext{Number}_2 = 14 	imes 840.
     $$  
   - Solve for the other number:  
     $$
     	ext{Number}_2 = \frac{14 	imes 840}{70} = 168.
     $$

Thus, the other number is **168**.

Answer

Answer

Answer