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Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had?
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Raju took some chocolates. He made groups with 5 of them and found out...
**Problem Analysis**
Let's assume that Raju had 'x' chocolates.
When Raju made groups of 5 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 5.
Similarly, when Raju made groups of 6 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 6.
And when Raju made groups of 8 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 8.
**Finding the Smallest Number**
To find the smallest number of chocolates Raju could have, we need to find the smallest number that satisfies all three conditions mentioned above.
We can start by finding the least common multiple (LCM) of the numbers 5, 6, and 8. LCM is the smallest multiple that is divisible by all the given numbers.
Let's find the LCM of 5, 6, and 8:
- Prime factors of 5: 5
- Prime factors of 6: 2, 3
- Prime factors of 8: 2, 2, 2
LCM = 5 * 2 * 2 * 2 * 3 = 120
So, the smallest number 'x' that satisfies all three conditions is 120.
**Explanation**
If Raju had 120 chocolates, he could make groups of 5, 6, and 8 chocolates.
- When he makes groups of 5 chocolates, there would be 24 groups of 5 chocolates (24 * 5 = 120), and 1 chocolate would be left.
- When he makes groups of 6 chocolates, there would be 20 groups of 6 chocolates (20 * 6 = 120), and 1 chocolate would be left.
- When he makes groups of 8 chocolates, there would be 15 groups of 8 chocolates (15 * 8 = 120), and 1 chocolate would be left.
So, the smallest number of chocolates Raju could have is 120.
Let's assume that Raju had 'x' chocolates.
When Raju made groups of 5 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 5.
Similarly, when Raju made groups of 6 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 6.
And when Raju made groups of 8 chocolates, he found out that 1 chocolate was left. This means that the number of chocolates 'x' is 1 more than a multiple of 8.
**Finding the Smallest Number**
To find the smallest number of chocolates Raju could have, we need to find the smallest number that satisfies all three conditions mentioned above.
We can start by finding the least common multiple (LCM) of the numbers 5, 6, and 8. LCM is the smallest multiple that is divisible by all the given numbers.
Let's find the LCM of 5, 6, and 8:
- Prime factors of 5: 5
- Prime factors of 6: 2, 3
- Prime factors of 8: 2, 2, 2
LCM = 5 * 2 * 2 * 2 * 3 = 120
So, the smallest number 'x' that satisfies all three conditions is 120.
**Explanation**
If Raju had 120 chocolates, he could make groups of 5, 6, and 8 chocolates.
- When he makes groups of 5 chocolates, there would be 24 groups of 5 chocolates (24 * 5 = 120), and 1 chocolate would be left.
- When he makes groups of 6 chocolates, there would be 20 groups of 6 chocolates (20 * 6 = 120), and 1 chocolate would be left.
- When he makes groups of 8 chocolates, there would be 15 groups of 8 chocolates (15 * 8 = 120), and 1 chocolate would be left.
So, the smallest number of chocolates Raju could have is 120.
Community Answer
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Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had?
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Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had?.
Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Raju took some chocolates. He made groups with 5 of them and found out 1 chocolate was left . He also tried making groups of 6 and 8 . And each time 1 chocolate was left over. What is the smallest number of chocolates did raju had?.
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