What is the least common multiple of 16 24 and 32

The first step to this method of finding the Least Common Multiple of 24 and 32 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.

Let’s take a look at the multiples for each of these numbers, 24 and 32:

What are the Multiples of 24?

What are the Multiples of 32?

Let’s take a look at the first 10 multiples for each of these numbers, 24 and 32:

First 10 Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240

First 10 Multiples of 32: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320

You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 24 and 32 are 96, 192, 288. Because 96 is the smallest, it is the least common multiple.

The LCM of 24 and 32 is 96.

The smallest positive number that is a multiple of two or more numbers.

Let's start with an Example ... 

List the Multiples of each number,

The multiples of 3 are 3, 6, 9, 12, 15, 18, ... etc
The multiples of 5 are 5, 10, 15, 20, 25, ... etc

Find the first Common (same) value:

The Least Common Multiple of 3 and 5 is 15

(15 is a multiple of both 3 and 5, and is the smallest number like that.)

So ... what is a "Multiple" ?

We get a multiple of a number when we multiply it by another number. Such as multiplying by 1, 2, 3, 4, 5, etc, but not zero. Just like the multiplication table.

Here are some examples:

What is a "Common Multiple" ?

Say we have listed the first few multiples of 4 and 5: the common multiples are those that are found in both lists:

Notice that 20 and 40 appear in both lists?
So, the common multiples of 4 and 5 are: 20, 40, (and 60, 80, etc ..., too)

What is the "Least Common Multiple" ?

It is simply the smallest of the common multiples.

In our previous example, the smallest of the common multiples is 20 ...

... so the Least Common Multiple of 4 and 5 is 20.

Finding the Least Common Multiple

List the multiples of the numbers until we get our first match.

The multiples of 4 are: 4, 8, 12, 16, 20, ...
and the multiples of 10 are: 10, 20, ...

Aha! there is a match at 20. It looks like this:

So the least common multiple of 4 and 10 is 20

The multiples of 6 are: 6, 12, 18, 24, 30, ...
and the multiples of 15 are: 15, 30, ...

There is a match at 30

So the least common multiple of 6 and 15 is 30

More than 2 Numbers

We can also find the least common multiple of three (or more) numbers.

Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
Multiples of 8 are: 8, 16, 24, 32, 40, ....

So 24 is the least common multiple (I can't find a smaller one!)

Hint: We can have smaller lists for the bigger numbers.

Least Common Multiple Tool

There is another method: the Least Common Multiple Tool does it automatically. (Yes, we waited until the end to tell you!)

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LCM of 16 and 24 is the smallest number among all common multiples of 16 and 24. The first few multiples of 16 and 24 are (16, 32, 48, 64, 80, 96, . . . ) and (24, 48, 72, 96, 120, 144, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 24 - by prime factorization, by listing multiples, and by division method.

What is the LCM of 16 and 24?

Answer: LCM of 16 and 24 is 48.

Explanation:

The LCM of two non-zero integers, x(16) and y(24), is the smallest positive integer m(48) that is divisible by both x(16) and y(24) without any remainder.

Methods to Find LCM of 16 and 24

Let's look at the different methods for finding the LCM of 16 and 24.

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

LCM of 16 and 24 by Division Method

To calculate the LCM of 16 and 24 by the division method, we will divide the numbers(16, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 24. Write this prime number(2) on the left of the given numbers(16 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 24) 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 16 and 24 is the product of all prime numbers on the left, i.e. LCM(16, 24) by division method = 2 × 2 × 2 × 2 × 3 = 48.

LCM of 16 and 24 by Prime Factorization

Prime factorization of 16 and 24 is (2 × 2 × 2 × 2) = 24 and (2 × 2 × 2 × 3) = 23 × 31 respectively. LCM of 16 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 31 = 48.
Hence, the LCM of 16 and 24 by prime factorization is 48.

LCM of 16 and 24 by Listing Multiples

To calculate the LCM of 16 and 24 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, . . . ) and 24 (24, 48, 72, 96, 120, 144, 168, . . . . )
• Step 2: The common multiples from the multiples of 16 and 24 are 48, 96, . . .
• Step 3: The smallest common multiple of 16 and 24 is 48.

∴ The least common multiple of 16 and 24 = 48.

☛ Also Check:

LCM of 16 and 24 Examples

1. Example 1: Verify the relationship between GCF and LCM of 16 and 24.

   Solution:

   The relation between GCF and LCM of 16 and 24 is given as, LCM(16, 24) × GCF(16, 24) = Product of 16, 24

   Prime factorization of 16 and 24 is given as, 16 = (2 × 2 × 2 × 2) = 24 and 24 = (2 × 2 × 2 × 3) = 23 × 31

   LCM(16, 24) = 48 GCF(16, 24) = 8 LHS = LCM(16, 24) × GCF(16, 24) = 48 × 8 = 384 RHS = Product of 16, 24 = 16 × 24 = 384 ⇒ LHS = RHS = 384

   Hence, verified.

Show Solution >

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The LCM of 16 and 24 is 48. To find the LCM of 16 and 24, we need to find the multiples of 16 and 24 (multiples of 16 = 16, 32, 48, 64; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 16 and 24, i.e., 48.

What is the Least Perfect Square Divisible by 16 and 24?

The least number divisible by 16 and 24 = LCM(16, 24)
LCM of 16 and 24 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 16 and 24 = LCM(16, 24) × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

If the LCM of 24 and 16 is 48, Find its GCF.

LCM(24, 16) × GCF(24, 16) = 24 × 16 Since the LCM of 24 and 16 = 48 ⇒ 48 × GCF(24, 16) = 384

Therefore, the greatest common factor = 384/48 = 8.

Which of the following is the LCM of 16 and 24? 30, 42, 21, 48

The value of LCM of 16, 24 is the smallest common multiple of 16 and 24. The number satisfying the given condition is 48.

What is the Relation Between GCF and LCM of 16, 24?

The following equation can be used to express the relation between GCF and LCM of 16 and 24, i.e. GCF × LCM = 16 × 24.