LCM of 16 and 22

LCM of 16 and 22 is the smallest number among all common multiples of 16 and 22. The first few multiples of 16 and 22 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (22, 44, 66, 88, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 22 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 16 and 22 is 176.

Explanation:

The LCM of two non-zero integers, x(16) and y(22), is the smallest positive integer m(176) that is divisible by both x(16) and y(22) without any remainder.

The methods to find the LCM of 16 and 22 are explained below.

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

LCM of 16 and 22 by Prime Factorization

Prime factorization of 16 and 22 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 11) = 2¹ × 11¹ respectively. LCM of 16 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 11¹ = 176.
Hence, the LCM of 16 and 22 by prime factorization is 176.

LCM of 16 and 22 by Listing Multiples

To calculate the LCM of 16 and 22 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 16 (16, 32, 48, 64, 80, 96, 112, . . . ) and 22 (22, 44, 66, 88, . . . . )
• Step 2: The common multiples from the multiples of 16 and 22 are 176, 352, . . .
• Step 3: The smallest common multiple of 16 and 22 is 176.

∴ The least common multiple of 16 and 22 = 176.

LCM of 16 and 22 by Division Method

To calculate the LCM of 16 and 22 by the division method, we will divide the numbers(16, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 22.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 22. Write this prime number(2) on the left of the given numbers(16 and 22), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 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 16 and 22 is the product of all prime numbers on the left, i.e. LCM(16, 22) by division method = 2 × 2 × 2 × 2 × 11 = 176.

☛ Also Check:

• LCM of 12 and 14 - 84
• LCM of 17 and 5 - 85
• LCM of 3, 5 and 7 - 105
• LCM of 15 and 90 - 90
• LCM of 60 and 72 - 360
• LCM of 10, 15 and 20 - 60
• LCM of 2 and 12 - 12

FAQs on LCM of 16 and 22

What is the LCM of 16 and 22?

The LCM of 16 and 22 is 176. To find the least common multiple (LCM) of 16 and 22, we need to find the multiples of 16 and 22 (multiples of 16 = 16, 32, 48, 64 . . . . 176; multiples of 22 = 22, 44, 66, 88 . . . . 176) and choose the smallest multiple that is exactly divisible by 16 and 22, i.e., 176.

What are the Methods to Find LCM of 16 and 22?

The commonly used methods to find the LCM of 16 and 22 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 22 and 16 is 176, Find its GCF.

LCM(22, 16) × GCF(22, 16) = 22 × 16
Since the LCM of 22 and 16 = 176
⇒ 176 × GCF(22, 16) = 352
Therefore, the greatest common factor (GCF) = 352/176 = 2.

What is the Relation Between GCF and LCM of 16, 22?

The following equation can be used to express the relation between GCF and LCM of 16 and 22, i.e. GCF × LCM = 16 × 22.

What is the Least Perfect Square Divisible by 16 and 22?

The least number divisible by 16 and 22 = LCM(16, 22)
LCM of 16 and 22 = 2 × 2 × 2 × 2 × 11 [Incomplete pair(s): 11]
⇒ Least perfect square divisible by each 16 and 22 = LCM(16, 22) × 11 = 1936 [Square root of 1936 = √1936 = ±44]
Therefore, 1936 is the required number.