LCM of 16 and 32

LCM of 16 and 32 is the smallest number among all common multiples of 16 and 32. The first few multiples of 16 and 32 are (16, 32, 48, 64, 80, . . . ) and (32, 64, 96, 128, 160, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 32 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 16 and 32 is 32.

Explanation:

The LCM of two non-zero integers, x(16) and y(32), is the smallest positive integer m(32) that is divisible by both x(16) and y(32) without any remainder.

The methods to find the LCM of 16 and 32 are explained below.

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

LCM of 16 and 32 by Listing Multiples

To calculate the LCM of 16 and 32 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, . . . ) and 32 (32, 64, 96, 128, 160, . . . . )
• Step 2: The common multiples from the multiples of 16 and 32 are 32, 64, . . .
• Step 3: The smallest common multiple of 16 and 32 is 32.

∴ The least common multiple of 16 and 32 = 32.

LCM of 16 and 32 by Division Method

To calculate the LCM of 16 and 32 by the division method, we will divide the numbers(16, 32) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 32.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 32. Write this prime number(2) on the left of the given numbers(16 and 32), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 32) 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 32 is the product of all prime numbers on the left, i.e. LCM(16, 32) by division method = 2 × 2 × 2 × 2 × 2 = 32.

LCM of 16 and 32 by Prime Factorization

Prime factorization of 16 and 32 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 2 × 2 × 2 × 2) = 2⁵ respectively. LCM of 16 and 32 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ = 32.
Hence, the LCM of 16 and 32 by prime factorization is 32.

☛ Also Check:

• LCM of 3, 5 and 6 - 30
• LCM of 16, 24 and 36 - 144
• LCM of 4 and 13 - 52
• LCM of 18 and 63 - 126
• LCM of 45 and 99 - 495
• LCM of 3 and 14 - 42
• LCM of 16, 28, 40 and 77 - 6160

FAQs on LCM of 16 and 32

What is the LCM of 16 and 32?

The LCM of 16 and 32 is 32. To find the LCM of 16 and 32, we need to find the multiples of 16 and 32 (multiples of 16 = 16, 32, 48, 64; multiples of 32 = 32, 64, 96, 128) and choose the smallest multiple that is exactly divisible by 16 and 32, i.e., 32.

What are the Methods to Find LCM of 16 and 32?

The commonly used methods to find the LCM of 16 and 32 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 32 and 16 is 32, Find its GCF.

LCM(32, 16) × GCF(32, 16) = 32 × 16
Since the LCM of 32 and 16 = 32
⇒ 32 × GCF(32, 16) = 512
Therefore, the greatest common factor (GCF) = 512/32 = 16.

What is the Least Perfect Square Divisible by 16 and 32?

The least number divisible by 16 and 32 = LCM(16, 32)
LCM of 16 and 32 = 2 × 2 × 2 × 2 × 2 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 16 and 32 = LCM(16, 32) × 2 = 64 [Square root of 64 = √64 = ±8]
Therefore, 64 is the required number.

How to Find the LCM of 16 and 32 by Prime Factorization?

To find the LCM of 16 and 32 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (32 = 2 × 2 × 2 × 2 × 2). LCM of 16 and 32 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 32.
⇒ LCM of 16, 32 = 2⁵ = 32.