Question

A natural number, when divided by 4, 5, 6, or 7, leaves a remainder of 3 in each case. What is the smallest of all such numbers?

• A. 843
• B. 213
• C. 423
• D. 63

Answer 1

Answer:

C. 423

Given:

Numbers = 4, 5, 6 or 7

Remainder when the number is divided with above numbers = 3

Concept used:

Find the LCM of the given numbers. 

LCM - smallest number which will be completely divisibly by the given numbers

For finding the number which will leave the remainder 3, will be (LCM + 3)

Calculation:

LCM of 4, 5, 6 and 7 = $7\times{5}\times{3}\times{2}\times{2}$ = 420

The number which will leave remainder 3 = 420 + 3

⇒ 423

Therefore the correct answer is 423.