LCM of 11 and 13

LCM of 11 and 13 is the smallest number among all common multiples of 11 and 13. The first few multiples of 11 and 13 are (11, 22, 33, 44, 55, 66, 77, . . . ) and (13, 26, 39, 52, 65, 78, . . . ) respectively. There are 3 commonly used methods to find LCM of 11 and 13 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 11 and 13 is 143.

Explanation:

The LCM of two non-zero integers, x(11) and y(13), is the smallest positive integer m(143) that is divisible by both x(11) and y(13) without any remainder.

Let's look at the different methods for finding the LCM of 11 and 13.

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

LCM of 11 and 13 by Listing Multiples

To calculate the LCM of 11 and 13 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, 55, 66, 77, . . . ) and 13 (13, 26, 39, 52, 65, 78, . . . . )
• Step 2: The common multiples from the multiples of 11 and 13 are 143, 286, . . .
• Step 3: The smallest common multiple of 11 and 13 is 143.

∴ The least common multiple of 11 and 13 = 143.

LCM of 11 and 13 by Division Method

To calculate the LCM of 11 and 13 by the division method, we will divide the numbers(11, 13) by their prime factors (preferably common). The product of these divisors gives the LCM of 11 and 13.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 11 and 13. Write this prime number(11) on the left of the given numbers(11 and 13), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (11, 13) is a multiple of 11, divide it by 11 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 13 is the product of all prime numbers on the left, i.e. LCM(11, 13) by division method = 11 × 13 = 143.

LCM of 11 and 13 by Prime Factorization

Prime factorization of 11 and 13 is (11) = 11¹ and (13) = 13¹ respectively. LCM of 11 and 13 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 11¹ × 13¹ = 143.
Hence, the LCM of 11 and 13 by prime factorization is 143.

☛ Also Check:

• LCM of 30 and 42 - 210
• LCM of 30 and 40 - 120
• LCM of 30 and 36 - 180
• LCM of 30 and 35 - 210
• LCM of 3 and 9 - 9
• LCM of 3 and 8 - 24
• LCM of 3 and 7 - 21

FAQs on LCM of 11 and 13

What is the LCM of 11 and 13?

The LCM of 11 and 13 is 143. To find the least common multiple (LCM) of 11 and 13, we need to find the multiples of 11 and 13 (multiples of 11 = 11, 22, 33, 44 . . . . 143; multiples of 13 = 13, 26, 39, 52 . . . . 143) and choose the smallest multiple that is exactly divisible by 11 and 13, i.e., 143.

If the LCM of 13 and 11 is 143, Find its GCF.

LCM(13, 11) × GCF(13, 11) = 13 × 11
Since the LCM of 13 and 11 = 143
⇒ 143 × GCF(13, 11) = 143
Therefore, the greatest common factor = 143/143 = 1.

What is the Least Perfect Square Divisible by 11 and 13?

The least number divisible by 11 and 13 = LCM(11, 13)
LCM of 11 and 13 = 11 × 13 [Incomplete pair(s): 11, 13]
⇒ Least perfect square divisible by each 11 and 13 = LCM(11, 13) × 11 × 13 = 20449 [Square root of 20449 = √20449 = ±143]
Therefore, 20449 is the required number.

What is the Relation Between GCF and LCM of 11, 13?

The following equation can be used to express the relation between GCF and LCM of 11 and 13, i.e. GCF × LCM = 11 × 13.

Which of the following is the LCM of 11 and 13? 24, 143, 27, 50

The value of LCM of 11, 13 is the smallest common multiple of 11 and 13. The number satisfying the given condition is 143.