LCM of 8 and 16

LCM of 8 and 16 is the smallest number among all common multiples of 8 and 16. The first few multiples of 8 and 16 are (8, 16, 24, 32, 40, 48, . . . ) and (16, 32, 48, 64, 80, 96, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 16 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 8 and 16 is 16.

Explanation:

The LCM of two non-zero integers, x(8) and y(16), is the smallest positive integer m(16) that is divisible by both x(8) and y(16) without any remainder.

The methods to find the LCM of 8 and 16 are explained below.

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

LCM of 8 and 16 by Division Method

To calculate the LCM of 8 and 16 by the division method, we will divide the numbers(8, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 16.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 16. Write this prime number(2) on the left of the given numbers(8 and 16), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 16 is the product of all prime numbers on the left, i.e. LCM(8, 16) by division method = 2 × 2 × 2 × 2 = 16.

LCM of 8 and 16 by Prime Factorization

Prime factorization of 8 and 16 is (2 × 2 × 2) = 2³ and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 8 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ = 16.
Hence, the LCM of 8 and 16 by prime factorization is 16.

LCM of 8 and 16 by Listing Multiples

To calculate the LCM of 8 and 16 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 16 (16, 32, 48, 64, 80, 96, 112, . . . . )
• Step 2: The common multiples from the multiples of 8 and 16 are 16, 32, . . .
• Step 3: The smallest common multiple of 8 and 16 is 16.

∴ The least common multiple of 8 and 16 = 16.

☛ Also Check:

• LCM of 11 and 13 - 143
• LCM of 72, 108 and 2100 - 37800
• LCM of 21 and 56 - 168
• LCM of 60 and 75 - 300
• LCM of 24 and 36 - 72
• LCM of 4 and 16 - 16
• LCM of 9 and 36 - 36

FAQs on LCM of 8 and 16

What is the LCM of 8 and 16?

The LCM of 8 and 16 is 16. To find the LCM of 8 and 16, we need to find the multiples of 8 and 16 (multiples of 8 = 8, 16, 24, 32; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 8 and 16, i.e., 16.

If the LCM of 16 and 8 is 16, Find its GCF.

LCM(16, 8) × GCF(16, 8) = 16 × 8
Since the LCM of 16 and 8 = 16
⇒ 16 × GCF(16, 8) = 128
Therefore, the GCF = 128/16 = 8.

What is the Least Perfect Square Divisible by 8 and 16?

The least number divisible by 8 and 16 = LCM(8, 16)
LCM of 8 and 16 = 2 × 2 × 2 × 2 [No incomplete pair]
⇒ Least perfect square divisible by each 8 and 16 = 16 [Square root of 16 = √16 = ±4]
Therefore, 16 is the required number.

How to Find the LCM of 8 and 16 by Prime Factorization?

To find the LCM of 8 and 16 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (16 = 2 × 2 × 2 × 2). LCM of 8 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 16.
⇒ LCM of 8, 16 = 2⁴ = 16.

What is the Relation Between GCF and LCM of 8, 16?

The following equation can be used to express the relation between GCF and LCM of 8 and 16, i.e. GCF × LCM = 8 × 16.