Question
Download Solution PDFDetermine the largest four-digit number that is exactly divisible by 15, 25, 40, and 75.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Determine the largest four-digit number that is exactly divisible by 15, 25, 40, and 75.
Formula used:
Find the LCM of 15, 25, 40, and 75
Calculation:
Prime factorization:
15 = 3 × 5
25 = 52
40 = 23 × 5
75 = 3 × 52
LCM = 23 × 3 × 52 = 600
Largest four-digit number = 9999
⇒ 9999 ÷ 600 = 16.665
⇒ Nearest integer quotient = 16
⇒ Largest four-digit number divisible by 600 = 600 × 16 = 9600
∴ The correct answer is option 1.
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