Find the greatest four digit number which is divisible by 3, 6, and 9.
2024
Find the greatest four digit number which is divisible by 3, 6, and 9.
Answer: B. 9990 — Concept: To find the greatest number (in a given range) that is divisible by several numbers together, first find the LCM of those numbers -- every multiple…
- A.
9999
- B.
9990
- C.
8899
- D.
7890
Attempted by 4 students.
Show answer & explanation
Correct answer: B
Concept: To find the greatest number (in a given range) that is divisible by several numbers together, first find the LCM of those numbers -- every multiple of the LCM is automatically divisible by each of them individually.
Find the LCM of 3, 6, and 9. Since 6 = 2×3 and 9 = 3×3, the LCM is 2×3×3 = 18.
The greatest four-digit number is 9999.
Divide 9999 by 18: 9999 = 18 × 555 + 9, so the remainder is 9.
Subtract the remainder from 9999 to get the largest multiple of 18 not exceeding it: 9999 − 9 = 9990.
Cross-check: the digit sum of 9990 is 9+9+9+0 = 27, which is divisible by both 3 and 9, and 9990 is even, so it is divisible by 6 as well -- confirming 9990 satisfies all three conditions and is exactly 18 × 555.