LCM of 13 and 11
LCM of 13 and 11 is the smallest number among all common multiples of 13 and 11. The first few multiples of 13 and 11 are (13, 26, 39, 52, 65, 78, 91, . . . ) and (11, 22, 33, 44, 55, 66, 77, . . . ) respectively. There are 3 commonly used methods to find LCM of 13 and 11  by prime factorization, by listing multiples, and by division method.
1.  LCM of 13 and 11 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 13 and 11?
Answer: LCM of 13 and 11 is 143.
Explanation:
The LCM of two nonzero integers, x(13) and y(11), is the smallest positive integer m(143) that is divisible by both x(13) and y(11) without any remainder.
Methods to Find LCM of 13 and 11
Let's look at the different methods for finding the LCM of 13 and 11.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 13 and 11 by Listing Multiples
To calculate the LCM of 13 and 11 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 13 (13, 26, 39, 52, 65, 78, 91, . . . ) and 11 (11, 22, 33, 44, 55, 66, 77, . . . . )
 Step 2: The common multiples from the multiples of 13 and 11 are 143, 286, . . .
 Step 3: The smallest common multiple of 13 and 11 is 143.
∴ The least common multiple of 13 and 11 = 143.
LCM of 13 and 11 by Division Method
To calculate the LCM of 13 and 11 by the division method, we will divide the numbers(13, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 13 and 11.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 13 and 11. Write this prime number(11) on the left of the given numbers(13 and 11), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (13, 11) 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 13 and 11 is the product of all prime numbers on the left, i.e. LCM(13, 11) by division method = 11 × 13 = 143.
LCM of 13 and 11 by Prime Factorization
Prime factorization of 13 and 11 is (13) = 13^{1} and (11) = 11^{1} respectively. LCM of 13 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 11^{1} × 13^{1} = 143.
Hence, the LCM of 13 and 11 by prime factorization is 143.
☛ Also Check:
 LCM of 3, 4 and 6  12
 LCM of 3, 4 and 5  60
 LCM of 3, 4 and 12  12
 LCM of 3, 4 and 9  36
 LCM of 3, 4 and 7  84
 LCM of 25, 40 and 60  600
 LCM of 24, 36 and 48  144
LCM of 13 and 11 Examples

Example 1: The GCD and LCM of two numbers are 1 and 143 respectively. If one number is 13, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 13 × z
⇒ z = (GCD × LCM)/13
⇒ z = (1 × 143)/13
⇒ z = 11
Therefore, the other number is 11. 
Example 2: Find the smallest number that is divisible by 13 and 11 exactly.
Solution:
The smallest number that is divisible by 13 and 11 exactly is their LCM.
⇒ Multiples of 13 and 11: Multiples of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, . . . .
 Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, . . . .
Therefore, the LCM of 13 and 11 is 143.

Example 3: Verify the relationship between GCF and LCM of 13 and 11.
Solution:
The relation between GCF and LCM of 13 and 11 is given as,
LCM(13, 11) × GCF(13, 11) = Product of 13, 11
Prime factorization of 13 and 11 is given as, 13 = (13) = 13^{1} and 11 = (11) = 11^{1}
LCM(13, 11) = 143
GCF(13, 11) = 1
LHS = LCM(13, 11) × GCF(13, 11) = 143 × 1 = 143
RHS = Product of 13, 11 = 13 × 11 = 143
⇒ LHS = RHS = 143
Hence, verified.
FAQs on LCM of 13 and 11
What is the LCM of 13 and 11?
The LCM of 13 and 11 is 143. To find the LCM of 13 and 11, we need to find the multiples of 13 and 11 (multiples of 13 = 13, 26, 39, 52 . . . . 143; multiples of 11 = 11, 22, 33, 44 . . . . 143) and choose the smallest multiple that is exactly divisible by 13 and 11, i.e., 143.
How to Find the LCM of 13 and 11 by Prime Factorization?
To find the LCM of 13 and 11 using prime factorization, we will find the prime factors, (13 = 13) and (11 = 11). LCM of 13 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 13 and 11.
⇒ LCM of 13, 11 = 11^{1} × 13^{1} = 143.
What is the Relation Between GCF and LCM of 13, 11?
The following equation can be used to express the relation between GCF and LCM of 13 and 11, i.e. GCF × LCM = 13 × 11.
If the LCM of 11 and 13 is 143, Find its GCF.
LCM(11, 13) × GCF(11, 13) = 11 × 13
Since the LCM of 11 and 13 = 143
⇒ 143 × GCF(11, 13) = 143
Therefore, the greatest common factor (GCF) = 143/143 = 1.
What are the Methods to Find LCM of 13 and 11?
The commonly used methods to find the LCM of 13 and 11 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
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