Question
Download Solution PDFHow many numbers less than 1,000 are multiples of both 7 and 11?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
We need to find how many numbers less than 1,000 are multiples of both 7 and 11.
Formula Used:
To find the multiples of two numbers, we use the Least Common Multiple (LCM).
Calculation:
LCM of 7 and 11:
7 and 11 are prime numbers.
LCM(7, 11) = 7 × 11 = 77
Now, we need to find how many multiples of 77 are less than 1,000.
Number of multiples of 77 less than 1,000 = ⌊1000 / 77⌋
⇒ ⌊1000 / 77⌋ = ⌊12.987…⌋
Since we take the floor value, we get 12.
Therefore, the number of numbers less than 1,000 that are multiples of both 7 and 11 is 12.
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