LCM of 8 and 11

LCM of 8 and 11 is the smallest number among all common multiples of 8 and 11. The first few multiples of 8 and 11 are (8, 16, 24, 32, . . . ) and (11, 22, 33, 44, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 11 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 8 and 11 is 88.

Explanation:

The LCM of two non-zero integers, x(8) and y(11), is the smallest positive integer m(88) that is divisible by both x(8) and y(11) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 11.

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

LCM of 8 and 11 by Prime Factorization

Prime factorization of 8 and 11 is (2 × 2 × 2) = 2³ and (11) = 11¹ respectively. LCM of 8 and 11 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 11¹ = 88.
Hence, the LCM of 8 and 11 by prime factorization is 88.

LCM of 8 and 11 by Division Method

To calculate the LCM of 8 and 11 by the division method, we will divide the numbers(8, 11) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 11.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 11. Write this prime number(2) on the left of the given numbers(8 and 11), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 11 is the product of all prime numbers on the left, i.e. LCM(8, 11) by division method = 2 × 2 × 2 × 11 = 88.

LCM of 8 and 11 by Listing Multiples

To calculate the LCM of 8 and 11 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, . . . ) and 11 (11, 22, 33, 44, . . . . )
• Step 2: The common multiples from the multiples of 8 and 11 are 88, 176, . . .
• Step 3: The smallest common multiple of 8 and 11 is 88.

∴ The least common multiple of 8 and 11 = 88.

☛ Also Check:

• LCM of 54 and 72 - 216
• LCM of 10 and 40 - 40
• LCM of 21 and 30 - 210
• LCM of 48, 56 and 72 - 1008
• LCM of 26 and 169 - 338
• LCM of 20 and 50 - 100
• LCM of 24, 30 and 40 - 120

FAQs on LCM of 8 and 11

What is the LCM of 8 and 11?

The LCM of 8 and 11 is 88. To find the LCM (least common multiple) of 8 and 11, we need to find the multiples of 8 and 11 (multiples of 8 = 8, 16, 24, 32 . . . . 88; multiples of 11 = 11, 22, 33, 44 . . . . 88) and choose the smallest multiple that is exactly divisible by 8 and 11, i.e., 88.

If the LCM of 11 and 8 is 88, Find its GCF.

LCM(11, 8) × GCF(11, 8) = 11 × 8
Since the LCM of 11 and 8 = 88
⇒ 88 × GCF(11, 8) = 88
Therefore, the GCF (greatest common factor) = 88/88 = 1.

What is the Least Perfect Square Divisible by 8 and 11?

The least number divisible by 8 and 11 = LCM(8, 11)
LCM of 8 and 11 = 2 × 2 × 2 × 11 [Incomplete pair(s): 2, 11]
⇒ Least perfect square divisible by each 8 and 11 = LCM(8, 11) × 2 × 11 = 1936 [Square root of 1936 = √1936 = ±44]
Therefore, 1936 is the required number.

How to Find the LCM of 8 and 11 by Prime Factorization?

To find the LCM of 8 and 11 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (11 = 11). LCM of 8 and 11 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 11.
⇒ LCM of 8, 11 = 2³ × 11¹ = 88.

What is the Relation Between GCF and LCM of 8, 11?

The following equation can be used to express the relation between GCF and LCM of 8 and 11, i.e. GCF × LCM = 8 × 11.