Question
Download Solution PDFHow many numbers are there from 17 to 457 which are divisible by both 5 and 3?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
If a number is divisible by both 5 and 3, it means that it's divisible by the least common multiple (LCM) of 5 and 3.
LCM(5, 3) = 15.
Now, we need to find how many numbers between 17 and 457 are divisible by 15. To do this, we can follow these steps:
Find the smallest multiple of 15 greater than or equal to 17. This is 30 (15 × 2).
Find the largest multiple of 15 less than or equal to 457. This is 450 (15 × 30).
Calculate the range of multiples between the smallest and largest multiples found above 450 - 30 = 420.
Divide the range by 15 and add 1 to get the number of multiples of 15: (420 / 15) + 1 = 28 + 1 = 29.
So, there are 29 numbers between 17 and 457 that are divisible by both 5 and 3.
∴ Option 1 is the correct answer.
Last updated on Jun 26, 2025
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