LCM of 5 and 22

LCM of 5 and 22 is the smallest number among all common multiples of 5 and 22. The first few multiples of 5 and 22 are (5, 10, 15, 20, 25, 30, 35, . . . ) and (22, 44, 66, 88, 110, 132, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 22 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 5 and 22 is 110.

Explanation:

The LCM of two non-zero integers, x(5) and y(22), is the smallest positive integer m(110) that is divisible by both x(5) and y(22) without any remainder.

The methods to find the LCM of 5 and 22 are explained below.

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

LCM of 5 and 22 by Listing Multiples

To calculate the LCM of 5 and 22 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, 35, . . . ) and 22 (22, 44, 66, 88, 110, 132, . . . . )
• Step 2: The common multiples from the multiples of 5 and 22 are 110, 220, . . .
• Step 3: The smallest common multiple of 5 and 22 is 110.

∴ The least common multiple of 5 and 22 = 110.

LCM of 5 and 22 by Prime Factorization

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

LCM of 5 and 22 by Division Method

To calculate the LCM of 5 and 22 by the division method, we will divide the numbers(5, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 22.

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

☛ Also Check:

• LCM of 30 and 70 - 210
• LCM of 48 and 120 - 240
• LCM of 11 and 22 - 22
• LCM of 30, 36 and 40 - 360
• LCM of 18, 24 and 36 - 72
• LCM of 12 and 25 - 300
• LCM of 16 and 64 - 64

FAQs on LCM of 5 and 22

What is the LCM of 5 and 22?

The LCM of 5 and 22 is 110. To find the LCM (least common multiple) of 5 and 22, we need to find the multiples of 5 and 22 (multiples of 5 = 5, 10, 15, 20 . . . . 110; multiples of 22 = 22, 44, 66, 88 . . . . 110) and choose the smallest multiple that is exactly divisible by 5 and 22, i.e., 110.

What is the Relation Between GCF and LCM of 5, 22?

The following equation can be used to express the relation between GCF and LCM of 5 and 22, i.e. GCF × LCM = 5 × 22.

If the LCM of 22 and 5 is 110, Find its GCF.

LCM(22, 5) × GCF(22, 5) = 22 × 5
Since the LCM of 22 and 5 = 110
⇒ 110 × GCF(22, 5) = 110
Therefore, the greatest common factor (GCF) = 110/110 = 1.

How to Find the LCM of 5 and 22 by Prime Factorization?

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

What are the Methods to Find LCM of 5 and 22?

The commonly used methods to find the LCM of 5 and 22 are:

• Division Method
• Prime Factorization Method
• Listing Multiples