Question

What is the smallest number which when divided by 64 and 80 leaves remainder 9 in each case?

• A. 337
• B. 329
• C. 320
• D. 311

Answer 1

Answer:

B. 329

Let the number be (N).

Given:

• $(N \div 64)\text{ leaves remainder} 9 ⇒ (N = 64k + 9)$

• (N \div 80) \text{leaves remainder 9 }⇒ (N = 80m + 9)

So,
$N - 9 \text{ is divisible by both } 64 \text{ and } 80$

Find LCM of 64 and 80

• $(64 = 2^6)$

• $(80 = 2^4 \times 5)$

LCM:
$2^6 \times 5 = 64 \times 5 = 320$

Find smallest number

N - 9 = 320
N = 320 + 9 = 329

Final Answer: 329