Hudson has a number of stamps that can be evenly separated into groups of 5,7, or 10. Find the number of stamps he might have. The number of stamps is a multiple of 70. The number of stamps is greater than 400. The number of stamps is a multiple of 50. The number of stamps is greater than 40.
Answers
Answer:
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Given:
Hudson has some number of stamps which can be equally divided into a group of 5,7 or 10 people.
To Find:
The total number of possible stamps.
Solution:
The given problem can be solved by using the concepts of LCM.
1. It is given that the stamps can be equally divided into a group of 5,7 or 10 people.
2. Since the stamps can be equally divided into a group of 5,7 or 10. It implies the remaining number of stamps is zero when they are divided into a group of 5,7 or 10 in an equal amount.
3. The least possible value which satisfies the above condition is the Least Common Multiple of 5, 7, and 10. The LCM of 5, 7, and 10 is 70.
4. Hence, the minimum number of stickers required is 70. The multiples of 70 can also satisfy the given case. Hence the total number of stickers will be 70 multiples.
5. The number of stickers can be greater than 400. ( Example 420 is a multiple of 70). The least possible case is 70 stickers, so the number of stickers is greater than 40.
Therefore, all of the mentioned statements are correct. The number of stickers Hudson has is 70 multiple.