LCM of 22 and 55

LCM of 22 and 55 is the smallest number among all common multiples of 22 and 55. The first few multiples of 22 and 55 are (22, 44, 66, 88, 110, 132, . . . ) and (55, 110, 165, 220, 275, . . . ) respectively. There are 3 commonly used methods to find LCM of 22 and 55 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 22 and 55 is 110.

Explanation:

The LCM of two non-zero integers, x(22) and y(55), is the smallest positive integer m(110) that is divisible by both x(22) and y(55) without any remainder.

Let's look at the different methods for finding the LCM of 22 and 55.

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

LCM of 22 and 55 by Listing Multiples

To calculate the LCM of 22 and 55 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 22 (22, 44, 66, 88, 110, 132, . . . ) and 55 (55, 110, 165, 220, 275, . . . . )
• Step 2: The common multiples from the multiples of 22 and 55 are 110, 220, . . .
• Step 3: The smallest common multiple of 22 and 55 is 110.

∴ The least common multiple of 22 and 55 = 110.

LCM of 22 and 55 by Prime Factorization

Prime factorization of 22 and 55 is (2 × 11) = 2¹ × 11¹ and (5 × 11) = 5¹ × 11¹ respectively. LCM of 22 and 55 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5¹ × 11¹ = 110.
Hence, the LCM of 22 and 55 by prime factorization is 110.

LCM of 22 and 55 by Division Method

To calculate the LCM of 22 and 55 by the division method, we will divide the numbers(22, 55) by their prime factors (preferably common). The product of these divisors gives the LCM of 22 and 55.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 22 and 55. Write this prime number(2) on the left of the given numbers(22 and 55), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (22, 55) 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 22 and 55 is the product of all prime numbers on the left, i.e. LCM(22, 55) by division method = 2 × 5 × 11 = 110.

☛ Also Check:

• LCM of 10 and 100 - 100
• LCM of 24, 36 and 54 - 216
• LCM of 5, 10, 15 and 30 - 30
• LCM of 16 and 64 - 64
• LCM of 11 and 18 - 198
• LCM of 3, 4 and 7 - 84
• LCM of 6, 9 and 12 - 36

FAQs on LCM of 22 and 55

What is the LCM of 22 and 55?

The LCM of 22 and 55 is 110. To find the least common multiple (LCM) of 22 and 55, we need to find the multiples of 22 and 55 (multiples of 22 = 22, 44, 66, 88 . . . . 110; multiples of 55 = 55, 110, 165, 220) and choose the smallest multiple that is exactly divisible by 22 and 55, i.e., 110.

If the LCM of 55 and 22 is 110, Find its GCF.

LCM(55, 22) × GCF(55, 22) = 55 × 22
Since the LCM of 55 and 22 = 110
⇒ 110 × GCF(55, 22) = 1210
Therefore, the greatest common factor = 1210/110 = 11.

How to Find the LCM of 22 and 55 by Prime Factorization?

To find the LCM of 22 and 55 using prime factorization, we will find the prime factors, (22 = 2 × 11) and (55 = 5 × 11). LCM of 22 and 55 is the product of prime factors raised to their respective highest exponent among the numbers 22 and 55.
⇒ LCM of 22, 55 = 2¹ × 5¹ × 11¹ = 110.

What are the Methods to Find LCM of 22 and 55?

The commonly used methods to find the LCM of 22 and 55 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

Which of the following is the LCM of 22 and 55? 10, 45, 21, 110

The value of LCM of 22, 55 is the smallest common multiple of 22 and 55. The number satisfying the given condition is 110.