LCM of 6 and 11

LCM of 6 and 11 is the smallest number among all common multiples of 6 and 11. The first few multiples of 6 and 11 are (6, 12, 18, 24, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 11 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 6 and 11 is 66.

Explanation:

The LCM of two non-zero integers, x(6) and y(11), is the smallest positive integer m(66) that is divisible by both x(6) and y(11) without any remainder.

The methods to find the LCM of 6 and 11 are explained below.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 6 and 11 by Prime Factorization

Prime factorization of 6 and 11 is (2 × 3) = 2¹ × 3¹ and (11) = 11¹ respectively. LCM of 6 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 11¹ = 66.
Hence, the LCM of 6 and 11 by prime factorization is 66.

LCM of 6 and 11 by Listing Multiples

To calculate the LCM of 6 and 11 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
• Step 2: The common multiples from the multiples of 6 and 11 are 66, 132, . . .
• Step 3: The smallest common multiple of 6 and 11 is 66.

∴ The least common multiple of 6 and 11 = 66.

LCM of 6 and 11 by Division Method

To calculate the LCM of 6 and 11 by the division method, we will divide the numbers(6, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 11.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 11. Write this prime number(2) on the left of the given numbers(6 and 11), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 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 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66.

☛ Also Check:

• LCM of 60 and 62 - 1860
• LCM of 24 and 32 - 96
• LCM of 15 and 90 - 90
• LCM of 13 and 52 - 52
• LCM of 8 and 13 - 104
• LCM of 40, 42 and 45 - 2520
• LCM of 11 and 15 - 165

FAQs on LCM of 6 and 11

What is the LCM of 6 and 11?

The LCM of 6 and 11 is 66. To find the least common multiple (LCM) of 6 and 11, we need to find the multiples of 6 and 11 (multiples of 6 = 6, 12, 18, 24 . . . . 66; multiples of 11 = 11, 22, 33, 44 . . . . 66) and choose the smallest multiple that is exactly divisible by 6 and 11, i.e., 66.

If the LCM of 11 and 6 is 66, Find its GCF.

LCM(11, 6) × GCF(11, 6) = 11 × 6
Since the LCM of 11 and 6 = 66
⇒ 66 × GCF(11, 6) = 66
Therefore, the GCF (greatest common factor) = 66/66 = 1.

What is the Least Perfect Square Divisible by 6 and 11?

The least number divisible by 6 and 11 = LCM(6, 11)
LCM of 6 and 11 = 2 × 3 × 11 [Incomplete pair(s): 2, 3, 11]
⇒ Least perfect square divisible by each 6 and 11 = LCM(6, 11) × 2 × 3 × 11 = 4356 [Square root of 4356 = √4356 = ±66]
Therefore, 4356 is the required number.

What are the Methods to Find LCM of 6 and 11?

The commonly used methods to find the LCM of 6 and 11 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

Which of the following is the LCM of 6 and 11? 2, 66, 5, 30

The value of LCM of 6, 11 is the smallest common multiple of 6 and 11. The number satisfying the given condition is 66.