LCM of 11 and 6

LCM of 11 and 6 is the smallest number among all common multiples of 11 and 6. The first few multiples of 11 and 6 are (11, 22, 33, 44, . . . ) and (6, 12, 18, 24, 30, 36, 42, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 6 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 11 and 6 is 66.

Explanation:

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

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

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

LCM of 11 and 6 by Division Method

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

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

LCM of 11 and 6 by Prime Factorization

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

LCM of 11 and 6 by Listing Multiples

To calculate the LCM of 11 and 6 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, . . . ) and 6 (6, 12, 18, 24, 30, 36, 42, . . . . )
• Step 2: The common multiples from the multiples of 11 and 6 are 66, 132, . . .
• Step 3: The smallest common multiple of 11 and 6 is 66.

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

☛ Also Check:

• LCM of 2 and 12 - 12
• LCM of 2 and 11 - 22
• LCM of 19 and 57 - 57
• LCM of 186 and 403 - 2418
• LCM of 18 and 72 - 72
• LCM of 18 and 63 - 126
• LCM of 18 and 54 - 54

FAQs on LCM of 11 and 6

What is the LCM of 11 and 6?

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

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

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

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

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

What is the Relation Between GCF and LCM of 11, 6?

The following equation can be used to express the relation between GCF and LCM of 11 and 6, i.e. GCF × LCM = 11 × 6.

How to Find the LCM of 11 and 6 by Prime Factorization?

To find the LCM of 11 and 6 using prime factorization, we will find the prime factors, (11 = 11) and (6 = 2 × 3). LCM of 11 and 6 is the product of prime factors raised to their respective highest exponent among the numbers 11 and 6.
⇒ LCM of 11, 6 = 2¹ × 3¹ × 11¹ = 66.