LCM of 3 and 11

LCM of 3 and 11 is the smallest number among all common multiples of 3 and 11. The first few multiples of 3 and 11 are (3, 6, 9, 12, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 11 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 3 and 11 is 33.

Explanation:

The LCM of two non-zero integers, x(3) and y(11), is the smallest positive integer m(33) that is divisible by both x(3) and y(11) without any remainder.

The methods to find the LCM of 3 and 11 are explained below.

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

LCM of 3 and 11 by Listing Multiples

To calculate the LCM of 3 and 11 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
• Step 2: The common multiples from the multiples of 3 and 11 are 33, 66, . . .
• Step 3: The smallest common multiple of 3 and 11 is 33.

∴ The least common multiple of 3 and 11 = 33.

LCM of 3 and 11 by Division Method

To calculate the LCM of 3 and 11 by the division method, we will divide the numbers(3, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 11.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 11. Write this prime number(3) on the left of the given numbers(3 and 11), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (3, 11) is a multiple of 3, divide it by 3 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 3 and 11 is the product of all prime numbers on the left, i.e. LCM(3, 11) by division method = 3 × 11 = 33.

LCM of 3 and 11 by Prime Factorization

Prime factorization of 3 and 11 is (3) = 3¹ and (11) = 11¹ respectively. LCM of 3 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 11¹ = 33.
Hence, the LCM of 3 and 11 by prime factorization is 33.

☛ Also Check:

• LCM of 12, 15 and 20 - 60
• LCM of 13 and 15 - 195
• LCM of 6 and 30 - 30
• LCM of 2, 3, 4, 5, and 6 - 60
• LCM of 404 and 96 - 9696
• LCM of 72 and 108 - 216
• LCM of 4, 5 and 7 - 140

FAQs on LCM of 3 and 11

What is the LCM of 3 and 11?

The LCM of 3 and 11 is 33. To find the least common multiple (LCM) of 3 and 11, we need to find the multiples of 3 and 11 (multiples of 3 = 3, 6, 9, 12 . . . . 33; multiples of 11 = 11, 22, 33, 44) and choose the smallest multiple that is exactly divisible by 3 and 11, i.e., 33.

What are the Methods to Find LCM of 3 and 11?

The commonly used methods to find the LCM of 3 and 11 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 11 and 3 is 33, Find its GCF.

LCM(11, 3) × GCF(11, 3) = 11 × 3
Since the LCM of 11 and 3 = 33
⇒ 33 × GCF(11, 3) = 33
Therefore, the GCF (greatest common factor) = 33/33 = 1.

Which of the following is the LCM of 3 and 11? 33, 30, 15, 5

The value of LCM of 3, 11 is the smallest common multiple of 3 and 11. The number satisfying the given condition is 33.

How to Find the LCM of 3 and 11 by Prime Factorization?

To find the LCM of 3 and 11 using prime factorization, we will find the prime factors, (3 = 3) and (11 = 11). LCM of 3 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 11.
⇒ LCM of 3, 11 = 3¹ × 11¹ = 33.