The Least Common Multiple (LCM) of 10 and 11 is a fundamental concept in Mathematics. This concept is crucial for solving various mathematical problems and understanding number theory. It is the smallest number that is a multiple of both 10 and 11. In this case, the LCM of 10 and 11 is 110. By understanding the concept of LCM, students can enhance their problem-solving skills and perform better in their exams. Let's dive into the process of calculating the LCM of 10 and 11.
LCM of 10 and 11 - Understanding and Calculating LCM
Last Updated on Jun 10, 2024
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Deciphering the LCM of 10 and 11
The Least Common Multiple of 10 and 11 is 110.
Methods to Calculate the LCM of 10 and 11
The LCM of 10 and 11 can be calculated using three principal methods:
- Prime Factorisation
- Division method
- Listing the multiples
Calculating LCM of 10 and 11 Using Prime Factorisation Method
The Prime Factorisation Method involves finding the prime factors of the numbers and multiplying the highest power of all the factors to find the LCM.
10 = 2 × 5
11 = 11
Hence, LCM (10, 11) = 2 × 5 × 11 = 110
Calculating LCM of 10 and 11 Using Division Method
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors to find the LCM.
| 2 | 10 | 11 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
The division process ends here.
Hence, LCM (10, 11) = 2 × 5 × 11 = 110
Calculating LCM of 10 and 11 by Listing the Multiples
This method involves listing the multiples of the numbers and finding the least common multiple.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, ……
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, …………
LCM (10, 11) = 110
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Examples
Q. 1: What is the smallest number that is divisible by both 12 and 13?
Solution: 156 is the smallest number that is divisible by both 12 and 13.
Q. 2: What is the LCM of 2, 3 and 4?
Solution: The LCM of 2, 3, and 4 is 12.
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Frequently Asked Questions
What is the LCM of 10 and 11?
The LCM of 10 and 11 is 110.
Is the LCM of 10 and 11 the same as the HCF of 10 and 11?
No. The LCM of 10 and 11 is 110 and the HCF of 10 and 11 is 1.
Is 120 the LCM of 10 and 11?
No. The LCM of 10 and 11 is 110.
Calculate the GCF if the LCM of 10 and 11 is 110.
The GCF of 10 and 11 is 1.
List the first five multiples of 10 and 11.
The first five multiples of 10 are: 10, 20, 30, 40, 50. The first five multiples of 11 are: 11, 22, 33, 44, 55.