To find the greatest 3-digit number divisible by 5, 15, 21, and 49, we need to find the LCM (Least Common Multiple) of these numbers and then find the greatest multiple of this LCM that is less than 1000.
Step 1: Find the LCM of 5, 15, 21, and 49
15 = 3 × 5
21 = 3 × 7
49 = 7²
So the LCM = 5 × 3 × 7² = 5 × 3 × 49 = 735
Step 2: Check if there's a larger multiple of 735 that is still a 3-digit number
735 × 2 = 1470, which exceeds 999 (the largest 3-digit number)
Therefore, 735 is the greatest 3-digit number that is divisible by 5, 15, 21, and 49.
