Find the greatest 5 digit number that is exactly divisible by 3, 4, 5 and 7?
2025
Find the greatest 5 digit number that is exactly divisible by 3, 4, 5 and 7?
- A.
99940
- B.
99960
- C.
99970
- D.
99990
Attempted by 23 students.
Show answer & explanation
Correct answer: B
Answer: 99960
Method:
Compute the LCM of 3, 4, 5 and 7: LCM(3,4)=12, LCM(12,5)=60, LCM(60,7)=420. So LCM = 420.
Take the largest 5-digit number, 99999, and divide by 420. The integer quotient is floor(99999 ÷ 420) = 238.
Multiply the quotient by the LCM: 238 × 420 = 99960. This is the largest 5-digit multiple of 420, so it is divisible by 3, 4, 5 and 7.
Check (optional): 99999 − 99960 = 39 (remainder), confirming 99960 is the greatest multiple below 99999.