Question

The smallest five digit number that is divisible by 22, 33 and 44 is:

• A. 10032
• B. 10042
• C. 10022
• D. 10132

Hint:

The required number must be a multiple of the LCM of the given divisors.

Answer 1

The Correct Option is A

Step 1: Concept
Find the LCM of the given numbers.

Step 2: Analysis
LCM of 22, 33, and 44: $22 = 2 \times 11$ $33 = 3 \times 11$ $44 = 2^{2} \times 11$ LCM $= 2^{2} \times 3 \times 11 = 4 \times 3 \times 11 = 132$.

Step 3: Calculation
Smallest 5-digit number is 10000. Divide 10000 by 132: $10000 \div 132 \approx 75.75$. The next multiple is $132 \times 76 = 10032$.

Step 4: Conclusion
Hence, the smallest five-digit number divisible by 22, 33, and 44 is 10032. Final Answer: (A)