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Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.?
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Determine the least number which when divided by 3 , 4 and 5 leaves re...
Problem: Determine the least number which when divided by 3, 4, and 5 leaves a remainder of 2 in each case.
Solution:
To solve this problem, we need to find the least common multiple (LCM) of 3, 4, and 5 and then add 2 to it.
Finding LCM:
We can find the LCM of 3, 4, and 5 by prime factorizing each number and then taking the highest power of each prime factor.
Prime factorization of 3: 3
Prime factorization of 4: 2 x 2
Prime factorization of 5: 5
So, the LCM of 3, 4, and 5 would be 2 x 2 x 3 x 5 = 60.
Adding Remainder:
Now, we add 2 to the LCM to get the required number.
60 + 2 = 62
Therefore, the least number which when divided by 3, 4, and 5 leaves a remainder of 2 in each case is 62.
Explanation:
When we divide 62 by 3, we get a remainder of 2. Similarly, when we divide 62 by 4 and 5, we also get a remainder of 2. This is because 62 is 2 more than the LCM of 3, 4, and 5, which means that it leaves a remainder of 2 when divided by each of these numbers.
Conclusion:
The required number is 62.
Solution:
To solve this problem, we need to find the least common multiple (LCM) of 3, 4, and 5 and then add 2 to it.
Finding LCM:
We can find the LCM of 3, 4, and 5 by prime factorizing each number and then taking the highest power of each prime factor.
Prime factorization of 3: 3
Prime factorization of 4: 2 x 2
Prime factorization of 5: 5
So, the LCM of 3, 4, and 5 would be 2 x 2 x 3 x 5 = 60.
Adding Remainder:
Now, we add 2 to the LCM to get the required number.
60 + 2 = 62
Therefore, the least number which when divided by 3, 4, and 5 leaves a remainder of 2 in each case is 62.
Explanation:
When we divide 62 by 3, we get a remainder of 2. Similarly, when we divide 62 by 4 and 5, we also get a remainder of 2. This is because 62 is 2 more than the LCM of 3, 4, and 5, which means that it leaves a remainder of 2 when divided by each of these numbers.
Conclusion:
The required number is 62.
Community Answer
Determine the least number which when divided by 3 , 4 and 5 leaves re...
You have to take firstly lcm of the given numbers means 3,4 and 5
so the lcm comes 60.
Now we have to add given remainder (2) = 62
So, the number comes 62.
PROOF-..
if we divide :- 62 by 3 remainder comes 2.
if we divide 62 by 4 remainder comes 2.
if we divide 62 by 5 remainder comes 2.
so the lcm comes 60.
Now we have to add given remainder (2) = 62
So, the number comes 62.
PROOF-..
if we divide :- 62 by 3 remainder comes 2.
if we divide 62 by 4 remainder comes 2.
if we divide 62 by 5 remainder comes 2.
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Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.?
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Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.?.
Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Determine the least number which when divided by 3 , 4 and 5 leaves remainder 2 in each case.?.
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