LCM of 2 and 11
LCM of 2 and 11 is the smallest number among all common multiples of 2 and 11. The first few multiples of 2 and 11 are (2, 4, 6, 8, 10, 12, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 11 - by division method, by prime factorization, and by listing multiples.
1. | LCM of 2 and 11 |
2. | List of Methods |
3. | Solved Examples |
4. | FAQs |
What is the LCM of 2 and 11?
Answer: LCM of 2 and 11 is 22.
![LCM of 2 and 11](https://static.qumath.in/static/website/old-cdn-static/common-factor/lcm-of-2-and-11.png)
Explanation:
The LCM of two non-zero integers, x(2) and y(11), is the smallest positive integer m(22) that is divisible by both x(2) and y(11) without any remainder.
Methods to Find LCM of 2 and 11
Let's look at the different methods for finding the LCM of 2 and 11.
- By Prime Factorization Method
- By Listing Multiples
- By Division Method
LCM of 2 and 11 by Prime Factorization
Prime factorization of 2 and 11 is (2) = 21 and (11) = 111 respectively. LCM of 2 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 111 = 22.
Hence, the LCM of 2 and 11 by prime factorization is 22.
LCM of 2 and 11 by Listing Multiples
To calculate the LCM of 2 and 11 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
- Step 2: The common multiples from the multiples of 2 and 11 are 22, 44, . . .
- Step 3: The smallest common multiple of 2 and 11 is 22.
∴ The least common multiple of 2 and 11 = 22.
LCM of 2 and 11 by Division Method
![LCM of 2 and 11 by Division Method](https://static.qumath.in/static/website/old-cdn-static/common-factor/lcm-of-2-and-11-by-division-method.png)
To calculate the LCM of 2 and 11 by the division method, we will divide the numbers(2, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 11.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 11. Write this prime number(2) on the left of the given numbers(2 and 11), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (2, 11) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
- Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 2 and 11 is the product of all prime numbers on the left, i.e. LCM(2, 11) by division method = 2 × 11 = 22.
☛ Also Check:
- LCM of 72 and 96 - 288
- LCM of 4 and 16 - 16
- LCM of 2, 4, 6, 8, 10 and 12 - 120
- LCM of 18 and 72 - 72
- LCM of 3, 4, 5 and 6 - 60
- LCM of 42 and 48 - 336
- LCM of 6 and 15 - 30
LCM of 2 and 11 Examples
-
Example 1: The GCD and LCM of two numbers are 1 and 22 respectively. If one number is 2, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 2 × z
⇒ z = (GCD × LCM)/2
⇒ z = (1 × 22)/2
⇒ z = 11
Therefore, the other number is 11. -
Example 2: Verify the relationship between GCF and LCM of 2 and 11.
Solution:
The relation between GCF and LCM of 2 and 11 is given as,
LCM(2, 11) × GCF(2, 11) = Product of 2, 11
Prime factorization of 2 and 11 is given as, 2 = (2) = 21 and 11 = (11) = 111
LCM(2, 11) = 22
GCF(2, 11) = 1
LHS = LCM(2, 11) × GCF(2, 11) = 22 × 1 = 22
RHS = Product of 2, 11 = 2 × 11 = 22
⇒ LHS = RHS = 22
Hence, verified. -
Example 3: Find the smallest number that is divisible by 2 and 11 exactly.
Solution:
The smallest number that is divisible by 2 and 11 exactly is their LCM.
⇒ Multiples of 2 and 11:- Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, . . . .
- Multiples of 11 = 11, 22, 33, 44, 55, 66, . . . .
Therefore, the LCM of 2 and 11 is 22.
FAQs on LCM of 2 and 11
What is the LCM of 2 and 11?
The LCM of 2 and 11 is 22. To find the least common multiple (LCM) of 2 and 11, we need to find the multiples of 2 and 11 (multiples of 2 = 2, 4, 6, 8 . . . . 22; multiples of 11 = 11, 22, 33, 44) and choose the smallest multiple that is exactly divisible by 2 and 11, i.e., 22.
If the LCM of 11 and 2 is 22, Find its GCF.
LCM(11, 2) × GCF(11, 2) = 11 × 2
Since the LCM of 11 and 2 = 22
⇒ 22 × GCF(11, 2) = 22
Therefore, the GCF = 22/22 = 1.
What is the Relation Between GCF and LCM of 2, 11?
The following equation can be used to express the relation between GCF and LCM of 2 and 11, i.e. GCF × LCM = 2 × 11.
Which of the following is the LCM of 2 and 11? 36, 5, 22, 35
The value of LCM of 2, 11 is the smallest common multiple of 2 and 11. The number satisfying the given condition is 22.
How to Find the LCM of 2 and 11 by Prime Factorization?
To find the LCM of 2 and 11 using prime factorization, we will find the prime factors, (2 = 2) and (11 = 11). LCM of 2 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 11.
⇒ LCM of 2, 11 = 21 × 111 = 22.
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