Given:
- LCM of two numbers = 7700
- HCF (GCD) of two numbers = 11
- One of the numbers = 2
We need to find the other number.
Step 1: Use the relationship between LCM, HCF, and the two numbers
For any two numbers aaa and bbb:
LCM(a,b)×HCF(a,b)=a×b\text{LCM}(a,b)\times \text{HCF}(a,b)=a\times bLCM(a,b)×HCF(a,b)=a×b
Let the other number be xxx. Given:
LCM=7700,HCF=11,a=2,b=x\text{LCM}=7700,\quad \text{HCF}=11,\quad a=2,\quad b=xLCM=7700,HCF=11,a=2,b=x
Substitute into the formula:
7700×11=2×x7700\times 11=2\times x7700×11=2×x
84700=2x84700=2x84700=2x
Step 2: Solve for xxx
x=847002=42350x=\frac{84700}{2}=42350x=284700=42350
Step 3: Verify the HCF condition
- The HCF is given as 11.
- Check if 11 divides both 2 and 42350.
Since 11 does not divide 2, this contradicts the given HCF.
Conclusion
The problem has an inconsistency because:
- If the HCF is 11, both numbers must be divisible by 11.
- But one number is 2, which is not divisible by 11.
Thus, there is no such number xxx that satisfies all the given conditions simultaneously. If you want, I can help you re-check the problem or clarify any part!
