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Find the least 5 digit number exactly divisible by 10,15,20,25?
Verified Answer
Find the least 5 digit number exactly divisible by 10,15,20,25?
Step-by-step explanation:
To find the least 5-digit number which is exactly divisible by 10, 15, 20 and 25, we have to first find the LCM of 10,15, 20 and 25.
10 = 2*5
15 = 5*3
20 = 5*2*2
25 = 5*5
LCM(10, 15, 20, 25)
= 5*5*2*2*3
= 300
So, LCM of 20, 25 and 30 is 300.
But we want the least 5 digit number, which is exactly divisible by 20, 25, 15 and 10.
Least 5 digit number = 10000.
10000 = 33 x 300 + 100
The next higher quotient is 34.
So, the required number = 34 x 300
= 10,200
This question is part of UPSC exam. View all Class 6 courses
Most Upvoted Answer
Find the least 5 digit number exactly divisible by 10,15,20,25?
Solution:
To find the least 5 digit number exactly divisible by 10, 15, 20, 25, we need to find their LCM.
Finding LCM:
Prime factorization of each number:
Highest power of each prime factor:
LCM: 2 x 2 x 5 x 5 x 3 = 300
Least 5 digit number: 10000
Finding the least 5 digit number:
Using the algorithm:
Therefore, the least 5 digit number exactly divisible by 10, 15, 20, and 25 is 10,000.
To find the least 5 digit number exactly divisible by 10, 15, 20, 25, we need to find their LCM.
Finding LCM:
- Prime factorize each number.
- Write down the highest power of each prime factor.
- Multiply the prime factors.
Prime factorization of each number:
- 10 = 2 x 5
- 15 = 3 x 5
- 20 = 2 x 2 x 5
- 25 = 5 x 5
Highest power of each prime factor:
- 2 x 2 x 5 x 5 = 100 (for 20 and 25)
- 3 (for 3)
LCM: 2 x 2 x 5 x 5 x 3 = 300
Least 5 digit number: 10000
Finding the least 5 digit number:
- Divide the LCM by the largest number (25).
- If the remainder is 0, then the LCM is the least number.
- If the remainder is not 0, then add the remainder to the LCM.
- Divide the new number by 24 (which is the product of the remaining numbers).
- If the remainder is 0, then the new number is the least number.
- If the remainder is not 0, then add the difference of 24 and the remainder to the new number.
Using the algorithm:
- Divide 300 by 25: The remainder is 0.
- 300 is the least number.
Therefore, the least 5 digit number exactly divisible by 10, 15, 20, and 25 is 10,000.
Community Answer
Find the least 5 digit number exactly divisible by 10,15,20,25?
5 by 15 × 10 by 25
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Find the least 5 digit number exactly divisible by 10,15,20,25?
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Find the least 5 digit number exactly divisible by 10,15,20,25? 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 5 digit number exactly divisible by 10,15,20,25? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least 5 digit number exactly divisible by 10,15,20,25?.
Find the least 5 digit number exactly divisible by 10,15,20,25? 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 5 digit number exactly divisible by 10,15,20,25? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the least 5 digit number exactly divisible by 10,15,20,25?.
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