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Choose the correct answer.A shopkeeper packed chocolates into bags of 48 and candies into bags of 150. He packed the same number of chocolates and candies. Find the least number of bags of candies the shopkeeper packed.5 bags of candies8 bags of candies3 bags of candies9 bags of candies

Question

Choose the correct answer.A shopkeeper packed chocolates into bags of 48 and candies into bags of 150. He packed the same number of chocolates and candies. Find the least number of bags of candies the shopkeeper packed.5 bags of candies8 bags of candies3 bags of candies9 bags of candies

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Solution

To solve this problem, we need to find the least common multiple (LCM) of 48 (the number of chocolates per bag) and 150 (the number of candies per bag). The LCM is the smallest number that both numbers divide into evenly.

  1. Prime factorize the two numbers:

    • 48 = 2^4 * 3
    • 150 = 2 * 3 * 5^2

  2. For each factor, take the highest power that appears in either factorization, and multiply these together:

    • LCM = 2^4 * 3 * 5^2 = 48 * 25 = 1200

  3. Since the shopkeeper packed the same number of chocolates and candies, he must have packed 1200 of each.

  4. To find the number of bags of candies, divide the total number of candies by the number of candies per bag:

    • Number of bags = 1200 / 150 = 8

So, the shopkeeper packed 8 bags of candies.

This problem has been solved

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