In between 150 AND 500 which is divisible by 2, 3, 7 ?
2025
In between 150 AND 500 which is divisible by 2, 3, 7 ?
- A.
8
- B.
4
- C.
6
- D.
10
Attempted by 20 students.
Show answer & explanation
Correct answer: A
Answer: 8 — number of integers between 150 and 500 divisible by 2, 3 and 7
Key idea: a number divisible by 2, 3 and 7 must be divisible by their LCM.
Step 1: Compute LCM(2, 3, 7) = 42.
Step 2: Find the first multiple of 42 greater than or equal to 150: 42 × 4 = 168.
Step 3: Find the last multiple of 42 less than or equal to 500: 42 × 11 = 462.
Step 4: Count the multiples from 42×4 to 42×11: 11 − 4 + 1 = 8.
Alternate check (using floor): floor(500/42) − floor(150/42) = 11 − 3 = 8, which matches the count above.
Therefore, there are 8 numbers between 150 and 500 that are divisible by 2, 3 and 7.