LCM of 2 and 16

LCM of 2 and 16 is the smallest number among all common multiples of 2 and 16. The first few multiples of 2 and 16 are (2, 4, 6, 8, 10, 12, . . . ) and (16, 32, 48, 64, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 16 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 2 and 16 is 16.

Explanation:

The LCM of two non-zero integers, x(2) and y(16), is the smallest positive integer m(16) that is divisible by both x(2) and y(16) without any remainder.

The methods to find the LCM of 2 and 16 are explained below.

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

LCM of 2 and 16 by Listing Multiples

To calculate the LCM of 2 and 16 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, . . . ) and 16 (16, 32, 48, 64, . . . . )
• Step 2: The common multiples from the multiples of 2 and 16 are 16, 32, . . .
• Step 3: The smallest common multiple of 2 and 16 is 16.

∴ The least common multiple of 2 and 16 = 16.

LCM of 2 and 16 by Division Method

To calculate the LCM of 2 and 16 by the division method, we will divide the numbers(2, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 16.

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

LCM of 2 and 16 by Prime Factorization

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

☛ Also Check:

• LCM of 35, 12 and 70 - 420
• LCM of 90 and 105 - 630
• LCM of 48 and 108 - 432
• LCM of 3, 5 and 10 - 30
• LCM of 8, 15 and 20 - 120
• LCM of 4, 6 and 12 - 12
• LCM of 15 and 35 - 105

FAQs on LCM of 2 and 16

What is the LCM of 2 and 16?

The LCM of 2 and 16 is 16. To find the LCM of 2 and 16, we need to find the multiples of 2 and 16 (multiples of 2 = 2, 4, 6, 8 . . . . 16; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 2 and 16, i.e., 16.

If the LCM of 16 and 2 is 16, Find its GCF.

LCM(16, 2) × GCF(16, 2) = 16 × 2
Since the LCM of 16 and 2 = 16
⇒ 16 × GCF(16, 2) = 32
Therefore, the greatest common factor = 32/16 = 2.

What is the Least Perfect Square Divisible by 2 and 16?

The least number divisible by 2 and 16 = LCM(2, 16)
LCM of 2 and 16 = 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 2 and 16 = 16 [Square root of 16 = √16 = ±4]
Therefore, 16 is the required number.

What is the Relation Between GCF and LCM of 2, 16?

The following equation can be used to express the relation between GCF and LCM of 2 and 16, i.e. GCF × LCM = 2 × 16.

How to Find the LCM of 2 and 16 by Prime Factorization?

To find the LCM of 2 and 16 using prime factorization, we will find the prime factors, (2 = 2) and (16 = 2 × 2 × 2 × 2). LCM of 2 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 16.
⇒ LCM of 2, 16 = 2⁴ = 16.