LCM of 16 and 18 is the smallest number among all common multiples of 16 and 18. The first few multiples of 16 and 18 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 18 - by prime factorization, by listing multiples, and by division method.

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1.LCM of 16 and 18
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 16 and 18 is 144.

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Explanation:

The LCM of two non-zero integers, x(16) and y(18), is the smallest positive integer m(144) that is divisible by both x(16) and y(18) without any remainder.


Let's look at the different methods for finding the LCM of 16 and 18.

By Listing MultiplesBy Prime Factorization MethodBy Division Method

LCM of 16 and 18 by Listing Multiples

To calculate the LCM of 16 and 18 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, 96, 112, . . . ) and 18 (18, 36, 54, 72, . . . . )Step 2: The common multiples from the multiples of 16 and 18 are 144, 288, . . .Step 3: The smallest common multiple of 16 and 18 is 144.

∴ The least common multiple of 16 and 18 = 144.

LCM of 16 and 18 by Prime Factorization

Prime factorization of 16 and 18 is (2 × 2 × 2 × 2) = 24 and (2 × 3 × 3) = 21 × 32 respectively. LCM of 16 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 32 = 144.Hence, the LCM of 16 and 18 by prime factorization is 144.

LCM of 16 and 18 by Division Method

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To calculate the LCM of 16 and 18 by the division method, we will divide the numbers(16, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 18.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 16 and 18 is the product of all prime numbers on the left, i.e. LCM(16, 18) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

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FAQs on LCM of 16 and 18

What is the LCM of 16 and 18?

The LCM of 16 and 18 is 144. To find the LCM (least common multiple) of 16 and 18, we need to find the multiples of 16 and 18 (multiples of 16 = 16, 32, 48, 64 . . . . 144; multiples of 18 = 18, 36, 54, 72 . . . . 144) and choose the smallest multiple that is exactly divisible by 16 and 18, i.e., 144.

How to Find the LCM of 16 and 18 by Prime Factorization?

To find the LCM of 16 and 18 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (18 = 2 × 3 × 3). LCM of 16 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 18.⇒ LCM of 16, 18 = 24 × 32 = 144.

If the LCM of 18 and 16 is 144, Find its GCF.

LCM(18, 16) × GCF(18, 16) = 18 × 16Since the LCM of 18 and 16 = 144⇒ 144 × GCF(18, 16) = 288Therefore, the greatest common factor = 288/144 = 2.

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What are the Methods to Find LCM of 16 and 18?

The commonly used methods to find the LCM of 16 and 18 are:

Division MethodListing MultiplesPrime Factorization Method

Which of the following is the LCM of 16 and 18? 15, 144, 50, 16

The value of LCM of 16, 18 is the smallest common multiple of 16 and 18. The number satisfying the given condition is 144.