LCM of 10 and 11

LCM of 10 and 11 is the smallest number among all common multiples of 10 and 11. The first few multiples of 10 and 11 are (10, 20, 30, 40, . . . ) and (11, 22, 33, 44, 55, 66, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 11 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 10 and 11 is 110.

Explanation:

The LCM of two non-zero integers, x(10) and y(11), is the smallest positive integer m(110) that is divisible by both x(10) and y(11) without any remainder.

The methods to find the LCM of 10 and 11 are explained below.

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

LCM of 10 and 11 by Prime Factorization

Prime factorization of 10 and 11 is (2 × 5) = 2¹ × 5¹ and (11) = 11¹ respectively. LCM of 10 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5¹ × 11¹ = 110.
Hence, the LCM of 10 and 11 by prime factorization is 110.

LCM of 10 and 11 by Division Method

To calculate the LCM of 10 and 11 by the division method, we will divide the numbers(10, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 11.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 11. Write this prime number(2) on the left of the given numbers(10 and 11), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 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 10 and 11 is the product of all prime numbers on the left, i.e. LCM(10, 11) by division method = 2 × 5 × 11 = 110.

LCM of 10 and 11 by Listing Multiples

To calculate the LCM of 10 and 11 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 10 (10, 20, 30, 40, . . . ) and 11 (11, 22, 33, 44, 55, 66, . . . . )
• Step 2: The common multiples from the multiples of 10 and 11 are 110, 220, . . .
• Step 3: The smallest common multiple of 10 and 11 is 110.

∴ The least common multiple of 10 and 11 = 110.

☛ Also Check:

• LCM of 8 and 30 - 120
• LCM of 8 and 28 - 56
• LCM of 8 and 25 - 200
• LCM of 8 and 22 - 88
• LCM of 8 and 20 - 40
• LCM of 8 and 18 - 72
• LCM of 8 and 16 - 16

FAQs on LCM of 10 and 11

What is the LCM of 10 and 11?

The LCM of 10 and 11 is 110. To find the least common multiple of 10 and 11, we need to find the multiples of 10 and 11 (multiples of 10 = 10, 20, 30, 40 . . . . 110; multiples of 11 = 11, 22, 33, 44 . . . . 110) and choose the smallest multiple that is exactly divisible by 10 and 11, i.e., 110.

If the LCM of 11 and 10 is 110, Find its GCF.

LCM(11, 10) × GCF(11, 10) = 11 × 10
Since the LCM of 11 and 10 = 110
⇒ 110 × GCF(11, 10) = 110
Therefore, the GCF (greatest common factor) = 110/110 = 1.

How to Find the LCM of 10 and 11 by Prime Factorization?

To find the LCM of 10 and 11 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (11 = 11). LCM of 10 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 11.
⇒ LCM of 10, 11 = 2¹ × 5¹ × 11¹ = 110.

What are the Methods to Find LCM of 10 and 11?

The commonly used methods to find the LCM of 10 and 11 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

Which of the following is the LCM of 10 and 11? 16, 20, 110, 27

The value of LCM of 10, 11 is the smallest common multiple of 10 and 11. The number satisfying the given condition is 110.