LCM of 8 and 22

LCM of 8 and 22 is the smallest number among all common multiples of 8 and 22. The first few multiples of 8 and 22 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (22, 44, 66, 88, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 22 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 8 and 22 is 88.

Explanation:

The LCM of two non-zero integers, x(8) and y(22), is the smallest positive integer m(88) that is divisible by both x(8) and y(22) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 22.

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

LCM of 8 and 22 by Listing Multiples

To calculate the LCM of 8 and 22 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, 40, 48, 56, . . . ) and 22 (22, 44, 66, 88, . . . . )
• Step 2: The common multiples from the multiples of 8 and 22 are 88, 176, . . .
• Step 3: The smallest common multiple of 8 and 22 is 88.

∴ The least common multiple of 8 and 22 = 88.

LCM of 8 and 22 by Division Method

To calculate the LCM of 8 and 22 by the division method, we will divide the numbers(8, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 22.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 22. Write this prime number(2) on the left of the given numbers(8 and 22), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 22) 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 22 is the product of all prime numbers on the left, i.e. LCM(8, 22) by division method = 2 × 2 × 2 × 11 = 88.

LCM of 8 and 22 by Prime Factorization

Prime factorization of 8 and 22 is (2 × 2 × 2) = 2³ and (2 × 11) = 2¹ × 11¹ respectively. LCM of 8 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 11¹ = 88.
Hence, the LCM of 8 and 22 by prime factorization is 88.

☛ Also Check:

• LCM of 42 and 63 - 126
• LCM of 4, 8 and 16 - 16
• LCM of 72, 126 and 168 - 504
• LCM of 12 and 21 - 84
• LCM of 6, 8 and 10 - 120
• LCM of 10, 12 and 15 - 60
• LCM of 15 and 27 - 135

FAQs on LCM of 8 and 22

What is the LCM of 8 and 22?

The LCM of 8 and 22 is 88. To find the least common multiple (LCM) of 8 and 22, we need to find the multiples of 8 and 22 (multiples of 8 = 8, 16, 24, 32 . . . . 88; multiples of 22 = 22, 44, 66, 88) and choose the smallest multiple that is exactly divisible by 8 and 22, i.e., 88.

Which of the following is the LCM of 8 and 22? 32, 42, 88, 5

The value of LCM of 8, 22 is the smallest common multiple of 8 and 22. The number satisfying the given condition is 88.

If the LCM of 22 and 8 is 88, Find its GCF.

LCM(22, 8) × GCF(22, 8) = 22 × 8
Since the LCM of 22 and 8 = 88
⇒ 88 × GCF(22, 8) = 176
Therefore, the greatest common factor (GCF) = 176/88 = 2.

What are the Methods to Find LCM of 8 and 22?

The commonly used methods to find the LCM of 8 and 22 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 8 and 22?

The least number divisible by 8 and 22 = LCM(8, 22)
LCM of 8 and 22 = 2 × 2 × 2 × 11 [Incomplete pair(s): 2, 11]
⇒ Least perfect square divisible by each 8 and 22 = LCM(8, 22) × 2 × 11 = 1936 [Square root of 1936 = √1936 = ±44]
Therefore, 1936 is the required number.