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LCM of 11 and 121
LCM of 11 and 121 is the smallest number among all common multiples of 11 and 121. The first few multiples of 11 and 121 are (11, 22, 33, 44, 55, . . . ) and (121, 242, 363, 484, 605, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 121  by listing multiples, by prime factorization, and by division method.
1.  LCM of 11 and 121 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 11 and 121?
Answer: LCM of 11 and 121 is 121.
Explanation:
The LCM of two nonzero integers, x(11) and y(121), is the smallest positive integer m(121) that is divisible by both x(11) and y(121) without any remainder.
Methods to Find LCM of 11 and 121
Let's look at the different methods for finding the LCM of 11 and 121.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 11 and 121 by Listing Multiples
To calculate the LCM of 11 and 121 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 11 (11, 22, 33, 44, 55, . . . ) and 121 (121, 242, 363, 484, 605, . . . . )
 Step 2: The common multiples from the multiples of 11 and 121 are 121, 242, . . .
 Step 3: The smallest common multiple of 11 and 121 is 121.
∴ The least common multiple of 11 and 121 = 121.
LCM of 11 and 121 by Prime Factorization
Prime factorization of 11 and 121 is (11) = 11^{1} and (11 × 11) = 11^{2} respectively. LCM of 11 and 121 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 11^{2} = 121.
Hence, the LCM of 11 and 121 by prime factorization is 121.
LCM of 11 and 121 by Division Method
To calculate the LCM of 11 and 121 by the division method, we will divide the numbers(11, 121) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 121.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 121. Write this prime number(11) on the left of the given numbers(11 and 121), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (11, 121) is a multiple of 11, divide it by 11 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 11 and 121 is the product of all prime numbers on the left, i.e. LCM(11, 121) by division method = 11 × 11 = 121.
☛ Also Check:
 LCM of 30 and 90  90
 LCM of 30 and 75  150
 LCM of 30 and 70  210
 LCM of 30 and 60  60
 LCM of 30 and 50  150
 LCM of 30 and 48  240
 LCM of 30 and 45  90
LCM of 11 and 121 Examples

Example 1: Verify the relationship between GCF and LCM of 11 and 121.
Solution:
The relation between GCF and LCM of 11 and 121 is given as,
LCM(11, 121) × GCF(11, 121) = Product of 11, 121
Prime factorization of 11 and 121 is given as, 11 = (11) = 11^{1} and 121 = (11 × 11) = 11^{2}
LCM(11, 121) = 121
GCF(11, 121) = 11
LHS = LCM(11, 121) × GCF(11, 121) = 121 × 11 = 1331
RHS = Product of 11, 121 = 11 × 121 = 1331
⇒ LHS = RHS = 1331
Hence, verified. 
Example 2: Find the smallest number that is divisible by 11 and 121 exactly.
Solution:
The smallest number that is divisible by 11 and 121 exactly is their LCM.
⇒ Multiples of 11 and 121: Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, . . . .
 Multiples of 121 = 121, 242, 363, 484, 605, 726, . . . .
Therefore, the LCM of 11 and 121 is 121.

Example 3: The GCD and LCM of two numbers are 11 and 121 respectively. If one number is 121, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 121 × p
⇒ p = (GCD × LCM)/121
⇒ p = (11 × 121)/121
⇒ p = 11
Therefore, the other number is 11.
FAQs on LCM of 11 and 121
What is the LCM of 11 and 121?
The LCM of 11 and 121 is 121. To find the least common multiple (LCM) of 11 and 121, we need to find the multiples of 11 and 121 (multiples of 11 = 11, 22, 33, 44 . . . . 121; multiples of 121 = 121, 242, 363, 484) and choose the smallest multiple that is exactly divisible by 11 and 121, i.e., 121.
If the LCM of 121 and 11 is 121, Find its GCF.
LCM(121, 11) × GCF(121, 11) = 121 × 11
Since the LCM of 121 and 11 = 121
⇒ 121 × GCF(121, 11) = 1331
Therefore, the greatest common factor = 1331/121 = 11.
Which of the following is the LCM of 11 and 121? 121, 32, 28, 40
The value of LCM of 11, 121 is the smallest common multiple of 11 and 121. The number satisfying the given condition is 121.
What are the Methods to Find LCM of 11 and 121?
The commonly used methods to find the LCM of 11 and 121 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
What is the Least Perfect Square Divisible by 11 and 121?
The least number divisible by 11 and 121 = LCM(11, 121)
LCM of 11 and 121 = 11 × 11 [No incomplete pair]
⇒ Least perfect square divisible by each 11 and 121 = 121 [Square root of 121 = √121 = ±11]
Therefore, 121 is the required number.
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