Question
Download Solution PDFA 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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 × 5 × 3 × 2 × 2 = 420
The number which will leave remainder 3 = 420 + 3
⇒ 423
Therefore the correct answer is 423.
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