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Find the least number when divided by 6,15,18 leave remainder 5 in each case?
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Find the least number when divided by 6,15,18 leave remainder 5 in eac...
Introduction:
To find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest multiple that is divisible by all the given numbers.
Step 1: Finding the LCM of 6, 15, and 18:
- Prime factorize each of the given numbers:
- 6 = 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
- Identify the common and uncommon prime factors:
- Common prime factors: 2 and 3
- Uncommon prime factors: 5
- Multiply the highest power of each prime factor to find the LCM:
- LCM = 2 * 3^2 * 5 = 90
Step 2: Adding the remainder:
Since we need to find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we need to add the remainder to the LCM.
- LCM + Remainder = 90 + 5 = 95
Therefore, the least number that leaves a remainder of 5 when divided by 6, 15, and 18 is 95.
Conclusion:
The least number that leaves a remainder of 5 when divided by 6, 15, and 18 is 95.
To find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest multiple that is divisible by all the given numbers.
Step 1: Finding the LCM of 6, 15, and 18:
- Prime factorize each of the given numbers:
- 6 = 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
- Identify the common and uncommon prime factors:
- Common prime factors: 2 and 3
- Uncommon prime factors: 5
- Multiply the highest power of each prime factor to find the LCM:
- LCM = 2 * 3^2 * 5 = 90
Step 2: Adding the remainder:
Since we need to find the least number that leaves a remainder of 5 when divided by 6, 15, and 18, we need to add the remainder to the LCM.
- LCM + Remainder = 90 + 5 = 95
Therefore, the least number that leaves a remainder of 5 when divided by 6, 15, and 18 is 95.
Conclusion:
The least number that leaves a remainder of 5 when divided by 6, 15, and 18 is 95.
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Find the least number when divided by 6,15,18 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers? 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 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers? 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 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers?.
Find the least number when divided by 6,15,18 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers? 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 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers? 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 leave remainder 5 in each case? Related: NCERT Solutions (Ex: 3.1 to 3.3): Playing with Numbers?.
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