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.

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

Answer: LCM of 6 and 16 is 48.

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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.


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

By Listing MultiplesBy Prime Factorization MethodBy Division Method

LCM of 6 and 16 by Listing Multiples

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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

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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 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.

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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 × 6Since the LCM of 16 and 6 = 48⇒ 48 × GCF(16, 6) = 96Therefore, 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 ⇒ Least perfect square divisible by each 6 and 16 = LCM(6, 16) × 3 = 144 Therefore, 144 is the required number.

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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.