Question

The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of the two numbers is 1:4, what is the larger of the two numbers?

• A. 30
• B. 25
• C. 60
• D. 108
• E. 84

Hint:

For two numbers, product = LCM $\times$ HCF. Use this relation along with the given ratio to find the numbers.

Answer 1

Answer: (E)

Step 1: Let the two numbers be $a$ and $b$, with $a : b = 1 : 4$. So $a = k$, $b = 4k$.
Step 2: For two numbers, product = LCM $\times$ HCF. So $a \times b = 84 \times 21 = 1764$.
Step 3: $(k)(4k) = 4k^2 = 1764 \implies k^2 = 441 \implies k = 21$.
Step 4: Then $a = 21$, $b = 84$. Larger number = 84.
Step 5: Check: LCM(21,84) = 84, HCF(21,84) = 21. Correct.
Step 6: Final Answer: The larger number is 84.