How many numbers less than 1,000 are multiples of both 7 and 11?

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SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 26 Jun, 2024 Shift 1)
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  1. 13
  2. 11
  3. 12
  4. 10

Answer (Detailed Solution Below)

Option 3 : 12
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Detailed Solution

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Given:

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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