Question
Download Solution PDFThe smallest number which when added to 10000 becomes divisible by 20, 24 and 30 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The smallest number which when added to 10000 becomes divisible by 20, 24, and 30.
Formula used:
Find LCM of 20, 24, and 30.
Calculation:
Prime Factorization:
20 = 22 × 5
24 = 23 × 3
30 = 2 × 3 × 5
LCM = 23 × 3 × 5 = 120
Find the smallest number added to 10000 that makes it divisible by 120:
10000 ÷ 120 = 83 remainder 40
To make the sum divisible by 120:
120 - 40 = 80
⇒ The smallest number is 80
∴ The correct answer is option (3).
Last updated on Jun 24, 2025
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