Multiple choice

Find the square of Z. Z is the remainder when the smallest 4-digit number exactly divisible by 24 and 36 is divided by 40?

  1. 144

  2. 36

  3. 100

  4. 64
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D Correct answer
Explanation

The smallest 4-digit number is 1000. Find LCM of 24 and 36: 24 = 2³ × 3, 36 = 2² × 3². LCM = 2³ × 3² = 8 × 9 = 72. Find the smallest 4-digit number divisible by 72: 1000 ÷ 72 = 13.89..., so we need 14 × 72 = 1008. The remainder when 1008 is divided by 40: 1008 ÷ 40 = 25.2, so 25 × 40 = 1000, remainder = 1008 - 1000 = 8. The square of 8 = 64.

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