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.

Answer: LCM of 7 and 11 is 77.

Explanation:

The LCM of two non-zero 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.

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) = 7¹ and (11) = 11¹ respectively. LCM of 7 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 7¹ × 11¹ = 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

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.