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LCM of 6 and 16

LCM of 6 and 16 is the smallest number among all common multiples of 6 and 16. The first few multiples of 6 and 16 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (16, 32, 48, 64, 80, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 16 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 6 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 6 and 16?

Answer: LCM of 6 and 16 is 48.

Explanation:

The LCM of two non-zero integers, x(6) and y(16), is the smallest positive integer m(48) that is divisible by both x(6) and y(16) without any remainder.

Methods to Find LCM of 6 and 16

The methods to find the LCM of 6 and 16 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 6 and 16 by Listing Multiples

To calculate the LCM of 6 and 16 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 16 (16, 32, 48, 64, 80, . . . . )
Step 2: The common multiples from the multiples of 6 and 16 are 48, 96, . . .
Step 3: The smallest common multiple of 6 and 16 is 48.

∴ The least common multiple of 6 and 16 = 48.

LCM of 6 and 16 by Prime Factorization

Prime factorization of 6 and 16 is (2 × 3) = 2¹ × 3¹ and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 6 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ = 48.
Hence, the LCM of 6 and 16 by prime factorization is 48.

LCM of 6 and 16 by Division Method

To calculate the LCM of 6 and 16 by the division method, we will divide the numbers(6, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 16.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 16. Write this prime number(2) on the left of the given numbers(6 and 16), separated as per the ladder arrangement.
Step 2: If any of the given numbers (6, 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 6 and 16 is the product of all prime numbers on the left, i.e. LCM(6, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.

☛ Also Check:

LCM of 6 and 16 Examples

Example 1: The product of two numbers is 96. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 96
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 96/2
Therefore, the LCM is 48.
The probable combination for the given case is LCM(6, 16) = 48.
Example 2: The GCD and LCM of two numbers are 2 and 48 respectively. If one number is 16, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 16 × z
⇒ z = (GCD × LCM)/16
⇒ z = (2 × 48)/16
⇒ z = 6
Therefore, the other number is 6.
Example 3: Verify the relationship between GCF and LCM of 6 and 16.

Solution:

The relation between GCF and LCM of 6 and 16 is given as,
LCM(6, 16) × GCF(6, 16) = Product of 6, 16
Prime factorization of 6 and 16 is given as, 6 = (2 × 3) = 2¹ × 3¹ and 16 = (2 × 2 × 2 × 2) = 2⁴
LCM(6, 16) = 48
GCF(6, 16) = 2
LHS = LCM(6, 16) × GCF(6, 16) = 48 × 2 = 96
RHS = Product of 6, 16 = 6 × 16 = 96
⇒ LHS = RHS = 96
Hence, verified.

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FAQs on LCM of 6 and 16

What is the LCM of 6 and 16?

The LCM of 6 and 16 is 48. To find the LCM of 6 and 16, we need to find the multiples of 6 and 16 (multiples of 6 = 6, 12, 18, 24 . . . . 48; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible by 6 and 16, i.e., 48.

What is the Relation Between GCF and LCM of 6, 16?

The following equation can be used to express the relation between GCF and LCM of 6 and 16, i.e. GCF × LCM = 6 × 16.

If the LCM of 16 and 6 is 48, Find its GCF.

LCM(16, 6) × GCF(16, 6) = 16 × 6
Since the LCM of 16 and 6 = 48
⇒ 48 × GCF(16, 6) = 96
Therefore, the greatest common factor (GCF) = 96/48 = 2.

What is the Least Perfect Square Divisible by 6 and 16?

The least number divisible by 6 and 16 = LCM(6, 16)
LCM of 6 and 16 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 6 and 16 = LCM(6, 16) × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

How to Find the LCM of 6 and 16 by Prime Factorization?

To find the LCM of 6 and 16 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (16 = 2 × 2 × 2 × 2). LCM of 6 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 16.
⇒ LCM of 6, 16 = 2⁴ × 3¹ = 48.

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