Question

The least number which when divided by 35, 56 and 91 leaves the same remainder 7 in each case will be:

• A. 3640
• B. 3645
• C. 3647
• D. 3740

Hint:

When the remainder is same, subtract the remainder first, find LCM, then add the remainder again.

Answer 1

The Correct Option is C

Step 1: Concept.
If a number leaves the same remainder when divided by multiple divisors, then the difference between that number and the remainder is a multiple of the LCM of those divisors.

Step 2: Find the LCM of 35, 56, and 91.
Prime factorization: 35 = 5 × 7
56 = 2³ × 7
91 = 7 × 13
\[ \text{LCM} = 2^3 \times 5 \times 7 \times 13 = 3640 \]
Step 3: Add the remainder (7).
\[ \text{Required number} = 3640 + 7 = 3647 \]
Step 4: Final answer.
\[ \text{Least number} = 3647 \]