How many numbers upto 400 are divisible by 4 and 3 together ?
2025
How many numbers upto 400 are divisible by 4 and 3 together ?
- A.
35
- B.
31
- C.
33
- D.
30
Attempted by 215 students.
Show answer & explanation
Correct answer: C
Answer: 33
Explanation: A number divisible by both 3 and 4 must be divisible by their least common multiple (LCM). The LCM of 3 and 4 is 12, so we need to count multiples of 12 that are ≤ 400.
Method 1 (division):
Compute floor(400 ÷ 12) = 33, so there are 33 multiples of 12 up to 400.
Method 2 (arithmetic progression):
The multiples of 12 up to 400 are: 12, 24, 36, ..., 396.
Use the formula for the nth term: last = first + (n − 1)·difference. So 396 = 12 + (n − 1)·12, which gives n = 33.