Question

LCM and HCF of two numbers are 182 and 13 respectively. If one number is 26, then other number will be :

• A. 13
• B. 39
• C. 78
• D. 91

Hint:

The HCF of two numbers is always a factor of their LCM. Here, $182 \div 13 = 14$, which confirms the data is consistent.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For any two positive integers $a$ and $b$, there is a fundamental relationship between their HCF and LCM: $a \times b = \text{HCF}(a,b) \times \text{LCM}(a,b)$.
Step 2: Identifying Given Values:

LCM = 182
HCF = 13
Number 1 ($a$) = 26
Number 2 ($b$) = ?
Step 3: Calculation:
$$26 \times b = 13 \times 182$$ $$b = \frac{13 \times 182}{26}$$ $$b = \frac{182}{2} = 91$$
Step 4: Final Answer:
The other number is 91.