What is the least amount that a person can have , such that when he…

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What is the least amount that a person can have , such that when he distributed it into groups of rs. 16 or rs. 18 or rs. 20 or rs. 25 he is always left with rs. 4?

  1. A.

    Rs. 2,245

  2. B.

    Rs. 2,615

  3. C.

    Rs. 3,604

  4. D.

    Rs. 2,475

Attempted by 219 students.

Show answer & explanation

Correct answer: C

Key idea: The required amount must leave remainder 4 when divided by 16, 18, 20 and 25, so subtracting 4 gives a number divisible by all four divisors.

  1. Let M = amount − 4. Then M must be a common multiple of 16, 18, 20 and 25.

  2. Compute the least common multiple (LCM) by prime factorization:

    • 16 = 2^4

    • 18 = 2 × 3^2

    • 20 = 2^2 × 5

    • 25 = 5^2

  3. Take the highest powers of each prime: 2^4, 3^2, 5^2. So LCM = 2^4 × 3^2 × 5^2 = 16 × 9 × 25 = 3600.

  4. Thus the smallest positive common multiple M is 3600, so the least amount is M + 4 = 3604.

Answer: Rs. 3,604

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