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Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case?
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Find the least number when divided by 6, 15,18 leaves a reminder of 5 ...
To find the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case, we have to find the L.C.M. of 6, 15 and 18 and then add 5 in that number.
L.C.M. of 6, 5 and 18
6 = 2*3
15 = 3*5
18 = 2*3*3
L.C.M. of 6, 15 and 18 = 2*3*3*5 = 90
Now,
5 + 90 = 95
Hence, 95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.
Let us check our answer.
1) 95/6
Quotient = 15
Remainder = 5
2) 95/15
Quotient = 6
Remainder = 5
3) 95/18
Quotient = 5
Remainder = 5
So, the required number is 95.
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Find the least number when divided by 6, 15,18 leaves a reminder of 5 ...
Finding the Least Number
To find the least number that when divided by 6, 15, and 18 leaves a remainder of 5 in each case, we need to look for the least common multiple of the divisors (6, 15, 18) and add 5 to it.
Finding the Least Common Multiple (LCM)
The LCM of 6, 15, and 18 can be calculated by finding the prime factors of each number:
- 6 = 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
Then, take the highest power of each prime factor:
- 2^1 * 3^2 * 5^1 = 90
Therefore, the LCM of 6, 15, and 18 is 90.
Adding the Remainder
To find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we add 5 to the LCM:
- 90 + 5 = 95
Therefore, the least number that when divided by 6, 15, and 18 leaves a remainder of 5 in each case is 95.
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Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case?
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Find the least number when divided by 6, 15,18 leaves a reminder of 5 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 Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case?.
Find the least number when divided by 6, 15,18 leaves a reminder of 5 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 Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least number when divided by 6, 15,18 leaves a reminder of 5 in each case?.
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