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Find the least positive integer which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2, when divided by 4 gives remainder 3 and when divided by 5 gives remainder 4?
- a)33
- b)59
- c)61
- d)49
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Find the least positive integer which when divided by 2 gives remainde...
Here the divisors are 2, 3, 4 and 5 and the respective remainders are 1, 2, 3 and 4.
The L.C.M. of (2, 3, 4, 5) = 60.
The least number satisfying the given condition = L.C.M. of (2, 3, 4, 5) – the difference between the divisor and the respective remainder. = 60 – 1 = 59
The L.C.M. of (2, 3, 4, 5) = 60.
The least number satisfying the given condition = L.C.M. of (2, 3, 4, 5) – the difference between the divisor and the respective remainder. = 60 – 1 = 59
Most Upvoted Answer
Find the least positive integer which when divided by 2 gives remainde...
Problem Analysis:
We need to find the least positive integer that satisfies the given conditions. Let's analyze the given conditions one by one:
1. When divided by 2, the integer gives a remainder of 1.
This means the integer is odd.
2. When divided by 3, the integer gives a remainder of 2.
This means the integer is 2 more than a multiple of 3.
3. When divided by 4, the integer gives a remainder of 3.
This means the integer is 3 more than a multiple of 4.
4. When divided by 5, the integer gives a remainder of 4.
This means the integer is 4 more than a multiple of 5.
Solution:
We need to find the least positive integer that satisfies all the given conditions. To do this, we can start with the smallest possible odd number (1) and check if it satisfies all the conditions. If it doesn't, we can increment the number by 2 and continue checking until we find a number that satisfies all the conditions.
Let's start with 1 and check if it satisfies the conditions:
1. When divided by 2, the remainder is 1. (Satisfied)
2. When divided by 3, the remainder is 2. (Satisfied)
3. When divided by 4, the remainder is 3. (Satisfied)
4. When divided by 5, the remainder is 4. (Satisfied)
Since 1 satisfies all the conditions, it is the least positive integer that satisfies the given conditions. Therefore, the answer is option B) 1.
Key Points:
- The least positive integer that satisfies the given conditions is 1.
We need to find the least positive integer that satisfies the given conditions. Let's analyze the given conditions one by one:
1. When divided by 2, the integer gives a remainder of 1.
This means the integer is odd.
2. When divided by 3, the integer gives a remainder of 2.
This means the integer is 2 more than a multiple of 3.
3. When divided by 4, the integer gives a remainder of 3.
This means the integer is 3 more than a multiple of 4.
4. When divided by 5, the integer gives a remainder of 4.
This means the integer is 4 more than a multiple of 5.
Solution:
We need to find the least positive integer that satisfies all the given conditions. To do this, we can start with the smallest possible odd number (1) and check if it satisfies all the conditions. If it doesn't, we can increment the number by 2 and continue checking until we find a number that satisfies all the conditions.
Let's start with 1 and check if it satisfies the conditions:
1. When divided by 2, the remainder is 1. (Satisfied)
2. When divided by 3, the remainder is 2. (Satisfied)
3. When divided by 4, the remainder is 3. (Satisfied)
4. When divided by 5, the remainder is 4. (Satisfied)
Since 1 satisfies all the conditions, it is the least positive integer that satisfies the given conditions. Therefore, the answer is option B) 1.
Key Points:
- The least positive integer that satisfies the given conditions is 1.
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Community Answer
Find the least positive integer which when divided by 2 gives remainde...
By using the trial and error method we can easily understand that the answer is option b) ie; 59. Use the bigger number ie; divide by 5 to eliminate unwanted options in a faster manner.
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Find the least positive integer which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2, when divided by 4 gives remainder 3 and when divided by 5 gives remainder 4?a)33 b)59 c)61 d)49Correct answer is option 'B'. Can you explain this answer?
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