LCM of 7 and 11
LCM of 7 and 11 is the smallest number among all common multiples of 7 and 11. The first few multiples of 7 and 11 are (7, 14, 21, 28, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 11  by prime factorization, by division method, and by listing multiples.
1.  LCM of 7 and 11 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 7 and 11?
Answer: LCM of 7 and 11 is 77.
Explanation:
The LCM of two nonzero integers, x(7) and y(11), is the smallest positive integer m(77) that is divisible by both x(7) and y(11) without any remainder.
Methods to Find LCM of 7 and 11
The methods to find the LCM of 7 and 11 are explained below.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 7 and 11 by Listing Multiples
To calculate the LCM of 7 and 11 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
 Step 2: The common multiples from the multiples of 7 and 11 are 77, 154, . . .
 Step 3: The smallest common multiple of 7 and 11 is 77.
∴ The least common multiple of 7 and 11 = 77.
LCM of 7 and 11 by Prime Factorization
Prime factorization of 7 and 11 is (7) = 7^{1} and (11) = 11^{1} respectively. LCM of 7 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7^{1} × 11^{1} = 77.
Hence, the LCM of 7 and 11 by prime factorization is 77.
LCM of 7 and 11 by Division Method
To calculate the LCM of 7 and 11 by the division method, we will divide the numbers(7, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 11.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 11. Write this prime number(7) on the left of the given numbers(7 and 11), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (7, 11) is a multiple of 7, divide it by 7 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 7 and 11 is the product of all prime numbers on the left, i.e. LCM(7, 11) by division method = 7 × 11 = 77.
☛ Also Check:
 LCM of 45 and 72  360
 LCM of 5 and 13  65
 LCM of 7 and 28  28
 LCM of 5 and 8  40
 LCM of 20, 25 and 30  300
 LCM of 36 and 54  108
 LCM of 3 and 13  39
LCM of 7 and 11 Examples

Example 1: Find the smallest number that is divisible by 7 and 11 exactly.
Solution:
The smallest number that is divisible by 7 and 11 exactly is their LCM.
⇒ Multiples of 7 and 11: Multiples of 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, . . . .
 Multiples of 11 = 11, 22, 33, 44, 55, 66, 77, . . . .
Therefore, the LCM of 7 and 11 is 77.

Example 2: Verify the relationship between GCF and LCM of 7 and 11.
Solution:
The relation between GCF and LCM of 7 and 11 is given as,
LCM(7, 11) × GCF(7, 11) = Product of 7, 11
Prime factorization of 7 and 11 is given as, 7 = (7) = 7^{1} and 11 = (11) = 11^{1}
LCM(7, 11) = 77
GCF(7, 11) = 1
LHS = LCM(7, 11) × GCF(7, 11) = 77 × 1 = 77
RHS = Product of 7, 11 = 7 × 11 = 77
⇒ LHS = RHS = 77
Hence, verified. 
Example 3: The product of two numbers is 77. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 77
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 77/1
Therefore, the LCM is 77.
The probable combination for the given case is LCM(7, 11) = 77.
FAQs on LCM of 7 and 11
What is the LCM of 7 and 11?
The LCM of 7 and 11 is 77. To find the LCM of 7 and 11, we need to find the multiples of 7 and 11 (multiples of 7 = 7, 14, 21, 28 . . . . 77; multiples of 11 = 11, 22, 33, 44 . . . . 77) and choose the smallest multiple that is exactly divisible by 7 and 11, i.e., 77.
What are the Methods to Find LCM of 7 and 11?
The commonly used methods to find the LCM of 7 and 11 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
If the LCM of 11 and 7 is 77, Find its GCF.
LCM(11, 7) × GCF(11, 7) = 11 × 7
Since the LCM of 11 and 7 = 77
⇒ 77 × GCF(11, 7) = 77
Therefore, the GCF (greatest common factor) = 77/77 = 1.
What is the Least Perfect Square Divisible by 7 and 11?
The least number divisible by 7 and 11 = LCM(7, 11)
LCM of 7 and 11 = 7 × 11 [Incomplete pair(s): 7, 11]
⇒ Least perfect square divisible by each 7 and 11 = LCM(7, 11) × 7 × 11 = 5929 [Square root of 5929 = √5929 = ±77]
Therefore, 5929 is the required number.
Which of the following is the LCM of 7 and 11? 21, 25, 10, 77
The value of LCM of 7, 11 is the smallest common multiple of 7 and 11. The number satisfying the given condition is 77.
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