What is the HCF and LCM of 84 and 144?

1. What is the LCM of 84 and 144?

Answer: LCM of 84 and 144 is 1008.

2. What are the Factors of 84?

Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.

3. What are the Factors of 144?

Answer: Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. There are 15 integers that are factors of 144. The greatest factor of 144 is 144.

4. How to Find the LCM of 84 and 144?

Answer:

Least Common Multiple of 84 and 144 = 1008

Step 1: Find the prime factorization of 84

84 = 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 144

144 = 2 x 2 x 2 x 2 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 84 and 144 is 1008.

Least Common Multiple Calculator

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Here you can find answers to questions like: What is the least common multiple of 84 and 144? or What is the LCM of 84 and 144?

Use this calculator to find the Least Common Multiple (LCM) for up to 3 mumbers.

The least common multiple (LCM) of a set of numbers is the lowest positive number that is a multiple of every number in that set.

Supose you want to find the Least Common Multiple (LCM) for 6 and 8, notation LCM(6,8):

The LCM of 6 and 8 is 24 because 24 is the smallest number that is both a multiple of 6 and a multiple of 8. This calculator uses the listing multiples method. This method consisits of writing out a list of the lowest multiples of each number, and look for the lowest multiple both numbers have in common. In this example we have:

• Multiples of 6: 6, 12, 18, 24. Note that 6 = 6 x 1, 12 = 6 x 2, 18 = 6 x 3, 24 = 6 x 4, 30 = 6 x 5
• Multiples of 8: 8, 16, 24. Also note that 8 = 8 x1, 16 = 8 x 2, 24 = 8 x 3, 32 = 8 x 4, ...

The LCM is also known as:

• lowest common multiple
• smallest common multiple

See also:

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While every effort is made to ensure the accuracy of the information provided on this website, neither this website nor its authors are responsible for any errors or omissions. Therefore, the contents of this site are not suitable for any use involving risk to health, finances or property.

The first step to this method of finding the Least Common Multiple of 144 and 84 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, 144 and 84:

What are the Multiples of 144?

What are the Multiples of 84?

Let’s take a look at the first 10 multiples for each of these numbers, 144 and 84:

First 10 Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440

First 10 Multiples of 84: 84, 168, 252, 336, 420, 504, 588, 672, 756, 840

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 144 and 84 are 1008, 2016, 3024. Because 1008 is the smallest, it is the least common multiple.

The LCM of 144 and 84 is 1008.

The LCM of 84 and 144 is 1008.

Steps to find LCM

1. Find the prime factorization of 84
   84 = 2 × 2 × 3 × 7
2. Find the prime factorization of 144
   144 = 2 × 2 × 2 × 2 × 3 × 3
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 2 × 2 × 2 × 3 × 3 × 7

4. LCM = 1008

MathStep (Works offline)

Find least common multiple (LCM) of: 168 & 288 42 & 72 252 & 432 28 & 48 420 & 720 588 & 1008 168 & 144 84 & 288 252 & 144 84 & 432 420 & 144 84 & 720 588 & 144 84 & 1008

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

HCF of 84 and 144 is the largest possible number that divides 84 and 144 exactly without any remainder. The factors of 84 and 144 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the HCF of 84 and 144 - long division, prime factorization, and Euclidean algorithm.

What is HCF of 84 and 144?

Answer: HCF of 84 and 144 is 12.

Explanation:

The HCF of two non-zero integers, x(84) and y(144), is the highest positive integer m(12) that divides both x(84) and y(144) without any remainder.

Methods to Find HCF of 84 and 144

The methods to find the HCF of 84 and 144 are explained below.

• Prime Factorization Method
• Long Division Method
• Using Euclid's Algorithm

HCF of 84 and 144 by Prime Factorization

Prime factorization of 84 and 144 is (2 × 2 × 3 × 7) and (2 × 2 × 2 × 2 × 3 × 3) respectively. As visible, 84 and 144 have common prime factors. Hence, the HCF of 84 and 144 is 2 × 2 × 3 = 12.

HCF of 84 and 144 by Long Division

HCF of 84 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 144 (larger number) by 84 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (84) by the remainder (60).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the HCF of 84 and 144.

HCF of 84 and 144 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 144 and Y = 84

• HCF(144, 84) = HCF(84, 144 mod 84) = HCF(84, 60)
• HCF(84, 60) = HCF(60, 84 mod 60) = HCF(60, 24)
• HCF(60, 24) = HCF(24, 60 mod 24) = HCF(24, 12)
• HCF(24, 12) = HCF(12, 24 mod 12) = HCF(12, 0)
• HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 84 and 144 is 12.

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HCF of 84 and 144 Examples

1. Example 1: The product of two numbers is 12096. If their HCF is 12, what is their LCM?

   Solution:

   Given: HCF = 12 and product of numbers = 12096 ∵ LCM × HCF = product of numbers ⇒ LCM = Product/HCF = 12096/12

   Therefore, the LCM is 1008.

Show Solution >

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The HCF of 84 and 144 is 12. To calculate the HCF (Highest Common Factor) of 84 and 144, we need to factor each number (factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the highest factor that exactly divides both 84 and 144, i.e., 12.

If the HCF of 144 and 84 is 12, Find its LCM.

HCF(144, 84) × LCM(144, 84) = 144 × 84 Since the HCF of 144 and 84 = 12 ⇒ 12 × LCM(144, 84) = 12096 Therefore, LCM = 1008

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What is the Relation Between LCM and HCF of 84, 144?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 84 and 144, i.e. HCF × LCM = 84 × 144.

How to Find the HCF of 84 and 144 by Long Division Method?

To find the HCF of 84, 144 using long division method, 144 is divided by 84. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 84 and 144?

There are three commonly used methods to find the HCF of 84 and 144.

• By Long Division
• By Listing Common Factors
• By Prime Factorization

How to Find the HCF of 84 and 144 by Prime Factorization?

To find the HCF of 84 and 144, we will find the prime factorization of the given numbers, i.e. 84 = 2 × 2 × 3 × 7; 144 = 2 × 2 × 2 × 2 × 3 × 3. ⇒ Since 2, 2, 3 are common terms in the prime factorization of 84 and 144. Hence, HCF(84, 144) = 2 × 2 × 3 = 12

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