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These LCM questions questions are specifically designed to enhance a sixth grader’s ability to find the smallest number that is a multiple of two or more numbers, which is particularly useful in real-life situations such as scheduling events or dividing resources evenly. LCM Questions for Class 6, students are introduced to methods for finding the LCM that include listing multiples or using the prime factorization approach. The exercises typically start with simple examples and gradually introduce more complex scenarios that require students to apply their understanding in diverse contexts. These problems not only bolster their mathematical skills but also improve their problem-solving abilities, preparing them for more advanced topics in mathematics.
What is LCM
LCM stands for Least Common Multiple. In simple words, it’s the smallest number that two or more numbers can both divide into evenly. For example, if you want to find the LCM of 4 and 6, it would be 12, because 12 is the smallest number that both 4 and 6 can divide into without leaving a remainder. LCM is especially useful when solving problems that involve adding or comparing fractions with different denominators.
How to Solve LCM Questions for Class 6
Solving Least Common Multiple (LCM) problems is a fundamental skill that students learn in Class 6. Understanding how to calculate the LCM helps in various mathematical contexts, such as simplifying fractions, adding and subtracting fractions with different denominators, and solving problems that involve multiples. Here is a step-by-step guide on how to solve LCM problems for Class 6:
Step 1: Understand the Concept
The Least Common Multiple of two or more numbers is the smallest number that is a multiple of all the numbers. It’s the smallest number that all the numbers divide into without leaving a remainder.
Step 2: Choose a Method
There are two main methods to find the LCM:
- Listing Multiples
- Prime Factorization
Method 1: Short Division Method
- Write the Numbers: Arrange the numbers horizontally at the top of your page.
- Divide by a Prime: Choose a prime number that can divide at least one of the numbers. Divide all numbers that are divisible by this prime, writing the result below each number.
- Repeat the Process: Continue the process with the results, using the same or another prime, until all the results are 1.
- Multiply the Primes: The LCM is the product of all the prime numbers used in the division.
Example: Find the LCM of 24 and 30.
- Write 24 and 30 at the top.
- Divide by 2 (prime number that divides both): Write 12 below 24 and 15
- 2 again (as it divides 12): Write 6 below 12 and 15 stays as it is (since 15 is not divisible by 2).
- Now divide by 3 (divides both 6 and 15): Write 2 below 6 and 5 below 15.
- Finally, divide by 2 and 5 respectively to get all results to 1: Write 1 below 2 and 1 below 5.
- The primes used were 2, 2, 3, 2, and 5. So, LCM = 2 × 2 × 3 × 2 × 5 = 120.
Method 2: Prime Factorization
- Factor Each Number: Break down each number into its prime factors.
- Use the Highest Power of Each Prime: For each prime number that appears in the factorization of any of the numbers, choose the highest power of that prime.
- Multiply the Highest Powers: The product of these numbers is the LCM.
Example: Find the LCM of 8 and 12.
- Prime factors of 8: 2³
- Prime factors of 12: 2², 3
- Use the highest power of each prime: 2³ and 3
- LCM = 2³ × 3 = 8 × 3 = 24
Step 3: Practice with Problems
Solve various problems that involve different sets of numbers. This practice will help solidify the methods and make finding the LCM an automatic process.
Step 4: Apply the LCM
Use the LCM to solve other types of problems, such as those involving adding fractions with different denominators, where finding the LCM of the denominators is essential for finding a common denominator.
LCM Questions for Class 6 with Answers
Here are LCM questions for class 6 with solutions based on short division method
LCM Questions Short Division Method
Question 1:
Find the LCM of 8 and 12.
Solution:
- Start with 8 and 12.
- Divide by 2: 4, 6
- Divide by 2: 2, 3
- Divide by 2: 1, 3
- Divide by 3: 1, 1
- LCM = 2 × 2 × 2 × 3 = 24
Question 2:
Find the LCM of 15 and 20.
Solution:
- Start with 15 and 20.
- Divide by 5: 3, 4
- Divide by 3: 1, 4
- Divide by 4: 1, 1
- LCM = 5 × 3 × 4 = 60
Question 3:
Find the LCM of 9 and 12.
Solution:
- Start with 9 and 12.
- Divide by 3: 3, 4
- Divide by 3: 1, 4
- Divide by 4: 1, 1
- LCM = 3 × 3 × 4 = 36
Question 4:
Find the LCM of 21 and 28.
Solution:
- Start with 21 and 28.
- Divide by 7: 3, 4
- Divide by 3: 1, 4
- Divide by 4: 1, 1
- LCM = 7 × 3 × 4 = 84
Question 5:
Find the LCM of 18 and 24.
Solution:
- Start with 18 and 24.
- Divide by 2: 9, 12
- Divide by 2: 9, 6
- Divide by 3: 3, 2
- Divide by 3: 1, 2
- Divide by 2: 1, 1
- LCM = 2 × 2 × 3 × 3 × 2 = 72
Question 6:
Find the LCM of 14 and 35.
Solution:
- Start with 14 and 35.
- Divide by 7: 2, 5
- Divide by 2: 1, 5
- Divide by 5: 1, 1
- LCM = 7 × 2 × 5 = 70
Question 7:
Find the LCM of 22 and 33.
Solution:
- Start with 22 and 33.
- Divide by 11: 2, 3
- Divide by 2: 1, 3
- Divide by 3: 1, 1
- LCM = 11 × 2 × 3 = 66
- Chapter 1 Knowing Our Numbers
- Chapter 2 Whole Numbers
- Chapter 3 Playing With Numbers
- Chapter 4 Basic Geometrical Ideas
- Chapter 5 Understanding Elementary Shapes
- Chapter 6 Integers
- Chapter 7 Fractions
- Chapter 8 Decimals
- Chapter 9 Data Handling
- Chapter 10 Mensuration
- Chapter 11 Algebra
- Chapter 12 Ratio and Proportion
- Chapter 13 Symmetry
- Chapter 14 Practical Geometry
Question 8:
Find the LCM of 25 and 30.
Solution:
- Start with 25 and 30.
- Divide by 5: 5, 6
- Divide by 5: 1, 6
- Divide by 2: 1, 3
- Divide by 3: 1, 1
- LCM = 5 × 5 × 2 × 3 = 150
Question 9:
Find the LCM of 16 and 20.
Solution:
- Start with 16 and 20.
- Divide by 2: 8, 10
- Divide by 2: 4, 5
- Divide by 2: 2, 5
- Divide by 2: 1, 5
- Divide by 5: 1, 1
- LCM = 2 × 2 × 2 × 2 × 5 = 80
Question 10:
Find the LCM of 13 and 17.
Solution:
- Start with 13 and 17.
- Since both are prime, LCM = 13 × 17 = 221
LCM Questions for Class 6 Prime Factorization Method
Here are LCM questions for Class 6 students with solutions using the Prime Factorization Method:
Question 1
Find the LCM of 8 and 12.
Solution:
- Prime factors of 8: 2³
- Prime factors of 12: 2² × 3
- LCM: Use the highest powers of all primes: 2³ × 3 = 24
Question 2
Calculate the LCM of 14 and 20.
Solution:
- Prime factors of 14: 2 × 7
- Prime factors of 20: 2² × 5
- LCM: Use the highest powers of all primes: 2² × 5 × 7 = 140
Question 3
Determine the LCM of 15 and 25.
Solution:
- Prime factors of 15: 3 × 5
- Prime factors of 25: 5²
- LCM: Use the highest powers of all primes: 3 × 5² = 75
Question 4
Find the LCM of 9 and 12.
Solution:
- Prime factors of 9: 3²
- Prime factors of 12: 2² × 3
- LCM: Use the highest powers of all primes: 2² × 3² = 36
Question 5
Calculate the LCM of 18 and 24.
Solution:
- Prime factors of 18: 2 × 3²
- Prime factors of 24: 2³ × 3
- LCM: Use the highest powers of all primes: 2³ × 3² = 72
Question 6
Determine the LCM of 10 and 15.
Solution:
- Prime factors of 10: 2 × 5
- Prime factors of 15: 3 × 5
- LCM: Use the highest powers of all primes: 2 × 3 × 5 = 30
Question 7
Find the LCM of 21 and 28.
Solution:
- Prime factors of 21: 3 × 7
- Prime factors of 28: 2² × 7
- LCM: Use the highest powers of all primes: 2² × 3 × 7 = 84
Question 8
Calculate the LCM of 22 and 33.
Solution:
- Prime factors of 22: 2 × 11
- Prime factors of 33: 3 × 11
- LCM: Use the highest powers of all primes: 2 × 3 × 11 = 66
Question 9
Determine the LCM of 35 and 49.
Solution:
- Prime factors of 35: 5 × 7
- Prime factors of 49: 7²
- LCM: Use the highest powers of all primes: 5 × 7² = 245
Question 10
Find the LCM of 16 and 20.
Solution:
- Prime factors of 16: 2⁴
- Prime factors of 20: 2² × 5
- LCM: Use the highest powers of all primes: 2⁴ × 5 = 80
Other Resources for Class 6 | |
Worksheet for Class 6 All subjects | CBSE Notes Class 6 |
NCERT Books for Class 6 | NCERT Solutions for Class 6 |
FAQs on LCM Questions for Class 6
What is an example of LCM for Class 6?
An example of LCM for Class 6 could be finding the Least Common Multiple of 12 and 18. Using the prime factorization method, the LCM is calculated as 36.
What is the HCF and LCM for Class 6?
In Class 6, HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts. HCF is the highest number that divides two or more numbers without leaving a remainder, whereas LCM is the smallest number that is a multiple of the given numbers.
What is the LCM of the fractions 2/5, 4/7, and 6/11?
To find the LCM of the fractions 2/5, 4/7, and 6/11, you look at the denominators: 5, 7, and 11. The LCM of these denominators using the prime factorization method is 385.
What is 6 and 18 LCM?
The LCM of 6 and 18 is 18. This is because 18 is the smallest number that both 6 and 18 can divide into without leaving a remainder.
What is the LCM of 25, 45, and 75?
The LCM of 25, 45, and 75 is 225. This is determined by finding the least common multiple of their prime factors: 5^{2}, 3^{2} × 5, and 3 × 5^{2}, resulting in 3^{2} × 5^{2}.