Question

The LCM of two numbers is 495 and their HCF is 5. If one of the numbers is 45, find the other number.

• A. 45
• B. 55
• C. 65
• D. 75

Hint:

Use the fact that HCF times LCM equals the product of the two numbers, approached through prime factorization and coprime cofactors rather than direct division.

Answer 1

The Correct Option is B

Step 1: Write $45=5\times9$, where $\text{HCF}=5$, so $\frac{45}{5}=9$ must be coprime to the corresponding cofactor of the other number.
Step 2: Let the other number $=5k$, where $k$ is coprime to $9$.
Step 3: Since $\text{LCM}=\text{HCF}\times(\text{coprime parts multiplied})=5\times9\times k=45k$, and LCM is given as 495: $45k=495\Rightarrow k=11$.
Step 4: Check: $\gcd(9,11)=1$, so this is valid. Other number $=5\times11=55$.
\[\boxed{55}\]