Ms. Santiago has many pens in her desk drawer. She says that if you divide the total number of pens by 1, 2, 3, 4, 5, or 6, you get a remainder of 1. What is the least number of pens that could be in ms. Santiago's drawer,
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Ms. Santiago has many pens in her desk drawer. She says that if you divide the total number of pens by 1, 2, 3, 4, 5, or 6, you get a remainder of 1. What is the least number of pens that could be in Ms. Santiago's drawer?
To find the least number of pens that could be in Ms. Santiago's drawer, we can start by considering the remainders when dividing the total number of pens by each of the given numbers: 1, 2, 3, 4, 5, and 6.
Let's go through each option and see if there is a pattern:
1. If we divide the total number of pens by 1, we will always get a remainder of 0 (since any number divided by 1 will have no remainder). So, this option does not satisfy the given condition of a remainder of 1.
2. If we divide the total number of pens by 2, we will get a remainder of 1 if the number is odd. For example, if there are 3 pens, dividing them by 2 gives us a remainder of 1: 3 ÷ 2 = 1 remainder 1. Therefore, to satisfy the condition, the total number of pens should be an odd number.
3. If we divide the total number of pens by 3, we will always get a remainder of 1 more than the remainder obtained when dividing by 2. So, if the remainder is 1 when dividing by 2, the remainder will be 2 when dividing by 3. If the remainder is 3 when dividing by 2, the remainder will be 4 when dividing by 3. This pattern continues. Therefore, to satisfy the condition, the remainder when dividing the total number of pens by 3 should be 1.
4. If we divide the total number of pens by 4, we will always get a remainder of 1 more than the remainder obtained when dividing by 2. For example, for 3 pens, the remainder when dividing by 2 is 1, and when dividing by 4, the remainder is also 1. This pattern continues. Therefore, to satisfy the condition, the remainder when dividing the total number of pens by 4 should be 1.
5. Similarly, if we divide the total number of pens by 5, we will always get a remainder of 1 more than the remainder obtained when dividing by 2. To satisfy the given condition, the remainder when dividing by 5 should be 1.
6. Lastly, if we divide the total number of pens by 6, we will always get a remainder of 1 more than the remainder obtained when dividing by 2. To satisfy the given condition, the remainder when dividing by 6 should be 1.
From the examination of the patterns, we can observe that the remainders when dividing the total number of pens by 2, 3, 4, 5, and 6 should all be 1. To find the lowest number that satisfies these conditions, we need to find the least common multiple (LCM) of 2, 3, 4, 5, and 6.
The LCM of 2, 3, 4, 5, and 6 is 60. Therefore, the least number of pens in Ms. Santiago's drawer could be 60.