RBSE Solutions Class 5 Maths Chapter 5 Multiples and Factors Exercise 5.1

Question 1. Write down 4 multiples of given numbers-
(i) 4
(ii) 7
(iii) 14
(iv) 19
Answer:
(i) The first four multiples of 4 are 8, 12, 16, and 20. Multiples are what you get when you multiply a number by whole numbers.
(ii) The first four multiples of 7 are 14, 21, 28, and 35.
(iii) The first four multiples of 14 are 28, 42, 56, and 70.
(iv) The first four multiples of 19 are 38, 57, 76, and 95.
In simple words: To find multiples, just count by that number several times. For example, for 4, count 4, 8, 12, 16, and so on.

🎯 Exam Tip: Remember that multiples are always equal to or greater than the number itself. The first multiple is always the number itself (e.g., 4 x 1 = 4).

Question 2. Circle only the multiples of the given number from the list.
(i) 3: 5, 9, 3, 13, 18
(ii) 5: 45, 11, 10, 22, 55
(iii) 12: 12, 36, 32, 48, 18
(iv) 15: 25, 35, 15, 40, 45
Answer:
(i) For 3: The multiples in the list are 9, 3, and 18.
(ii) For 5: The multiples in the list are 45, 10, and 55.
(iii) For 12: The multiples in the list are 12, 36, and 48.
(iv) For 15: The multiples in the list are 15 and 45. A number is a multiple if it can be divided by the given number without a remainder.
In simple words: Look at each number in the list. If you can divide it perfectly by the given number (like 3 or 5), then it's a multiple.

🎯 Exam Tip: To check if a number is a multiple, you can divide it by the given number. If there is no remainder, it is a multiple.

Question 4. Write the multiples of 7 which lie between 10 and 30.
Answer: The multiples of 7 are found by multiplying 7 by counting numbers. We need the multiples of 7 that are bigger than 10 but smaller than 30.
\( 7 \times 1 = 7 \) (too small)
\( 7 \times 2 = 14 \)
\( 7 \times 3 = 21 \)
\( 7 \times 4 = 28 \)
\( 7 \times 5 = 35 \) (too big)
So, the multiples of 7 between 10 and 30 are 14, 21, and 28.
In simple words: We list numbers you get by counting in sevens, but only pick the ones that are between 10 and 30. These are 14, 21, and 28.

🎯 Exam Tip: When asked for numbers "between" two values, exclude the start and end values themselves unless specifically told to include them.

Question 5. Write three multiples of 4, which are greater than 25.
Answer: We need to find multiples of 4 that are larger than 25. Let's list multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and so on. The first three multiples that are greater than 25 are 28, 32, and 36.
In simple words: We count by fours and pick the first three numbers that are bigger than 25. These are 28, 32, and 36.

🎯 Exam Tip: Start listing multiples from the number itself and continue until you find the ones that meet the given condition (e.g., "greater than 25").

Question 6. Find out the least common multiple (LCM) of 2 and 5.
Answer: To find the Least Common Multiple (LCM), we list the multiples of each number until we find the smallest one they share.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
The smallest number that appears in both lists is 10. Thus, the least common multiple of 2 and 5 is 10.
In simple words: We list numbers that can be divided by 2, and then list numbers that can be divided by 5. The smallest number that appears in both lists is called the Least Common Multiple (LCM), which is 10.

🎯 Exam Tip: The LCM is useful for adding and subtracting fractions because it helps find a common denominator.

Question 7. Find out the least common multiple (LCM) of 8 and 12.
Answer: We will list the multiples of 8 and 12 to find their Least Common Multiple (LCM).
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Multiples of 12: 12, 24, 36, 48, 60, ...
The common multiples of 8 and 12 are 24, 48, and so on. The smallest of these common multiples is 24. So, the least common multiple of 8 and 12 is 24.
In simple words: We write down multiples for 8 and multiples for 12. The smallest number that is in both lists is 24, which is their LCM.

🎯 Exam Tip: Always make sure to list enough multiples for both numbers to clearly identify the first common multiple.

Question 8. Find out the least common multiple (LCM) of 6, 9 and 15.
Answer: To find the least common multiple of 6, 9, and 15, we can list their multiples:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, ...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, ...
The least common multiple of 6, 9, and 15 is 90. This means 90 is the smallest number that can be perfectly divided by 6, 9, and 15.
In simple words: We list numbers that 6, 9, and 15 can all divide into. The smallest such number is 90.

🎯 Exam Tip: For three numbers, list the multiples of the largest number first, then check if the smaller numbers divide into them until you find a match.

Question 1. List the factors of 6, 8, and 15.
Answer: Factors are numbers that divide another number exactly, without leaving a remainder.
Factors of 6: The numbers that divide 6 completely are 1, 2, 3, and 6.
Factors of 8: The numbers that divide 8 completely are 1, 2, 4, and 8.
Factors of 15: The numbers that divide 15 completely are 1, 3, 5, and 15. Every number has at least two factors: 1 and itself.
In simple words: Factors are numbers you can multiply together to get another number. For example, for 6, you can do \( 1 \times 6 \) or \( 2 \times 3 \). So, 1, 2, 3, 6 are its factors.

🎯 Exam Tip: Always remember to include 1 and the number itself in the list of factors. It helps to check factor pairs (e.g., for 12: \( 1 \times 12 \), \( 2 \times 6 \), \( 3 \times 4 \)).

Question 2. Find out the factors of 9 and 27. Write their common factors too and identify the highest common factor (HCF).
Answer: We need to find the factors for both numbers, then see which factors they share, and finally, identify the largest shared factor.
Factors of 9: 1, 3, 9.
Factors of 27: 1, 3, 9, 27.
The numbers that are factors of both 9 and 27 are 1, 3, and 9. These are called common factors.
The highest (largest) common factor (HCF) among 1, 3, and 9 is 9. This means 9 is the biggest number that divides both 9 and 27 perfectly.

In simple words: First, find all the numbers that can divide 9. Then do the same for 27. The numbers found in both lists are common factors. The biggest number that is common is the Highest Common Factor (HCF), which is 9.
🎯 Exam Tip: Listing all factors for each number and then circling the common ones is a reliable method to find both common factors and the HCF.