Question
Download Solution PDFHow many natural numbers between 1 and 500 are divisible by each of the numbers 3, 5 and 7?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
To determine how many natural numbers between 1 and 500 are divisible by multiple numbers (in this case, 3, 5, and 7), we need to find the least common multiple (LCM) of these numbers. Once we have the LCM, we can count how many multiples of this LCM exist within the given range.
Calculation:
LCM Calculation:
LCM of 3, 5, and 7: Since 3, 5, and 7 are all prime numbers, their LCM is simply their product: 3 × 5 × 7 = 105.
Counting Multiples:
To find how many multiples of 105 are there between 1 and 500, we divide the upper limit (500) by the LCM (105).
Number of multiples = 500 / 105 ≈ 4.76
Since we're looking for whole numbers, we take the integer part of the division: 4.
Thus, 4 natural numbers between 1 and 500 are divisible by 3, 5, and 7.
∴ The Correct answer is Option (4): 4
Last updated on Apr 30, 2025
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