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LCM

How To Find LCM of 63, 70, and 77? | Listing, Division, and Prime Factorization Method

Written by Prerit Jain

Updated on: 17 Feb 2023

How To Find LCM of 63, 70, and 77? | Listing, Division, and Prime Factorization Method

How To Find LCM of 63, 70, and 77? | Listing, Division, and Prime Factorization Method

LCM of 63, 70, and 77 is 6930. LCM of 63, 70, and 77, also known as the Least Common Multiple or Lowest Common Multiple of 63, 70, and 77 is the lowest possible common number that is divisible by 63, 70, and 77.

Now, let’s see how to find the LCM of 63, 70, and 77. 
Multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567, 630,…,6804, 6867, 6930, 6993, 7056,…
Multiples of 70 are 70, 140, 210, 280, 350, 420, 490, 560, 630, 700,…,6790, 6860, 6930, 7000, 7070, 7140,…
Multiples of 77 are 77, 154, 231, 308, 385, 462, 539, 616, 693, 770,…,6776, 6853, 6930, 7007, 7084, 7161,… 
Here, 6930 is the common number in the multiples of 63, 70, and 77, respectively, or that are divisible by 63, 70, and 77. So, 6930 is the lowest common number among all the multiples that is divisible by 63, 70, and 77, and hence the LCM of 63, 70, and 77 is 6930.

How to Find the LCM of 63, 70, and 77

There are three different methods for finding the LCM of 63, 70, and 77. These methods are:

1. Prime Factorization Method 
2. Listing Method 
3. Division Method  

Finding LCM of 63, 70, and 77 Using the Prime Factorization Method

The prime factorization method is one of the methods for finding the LCM. To find the LCM of 63, 70, and 77 using the prime factorization method, follow the following steps:

Step 1: Find the prime factors of 63, 70, and 77 using the repeated division method.
Step 2: Write all the prime factors in their exponent forms. Then multiply the prime factors having the highest power.
Step 3: The final result after multiplication will be the LCM of 63, 70, and 77.

LCM of 63, 70, and 77 can be obtained using the prime factorization method as

  • Prime factorization of 63 can be expressed as 3 * 3 * 7 = 31 * 31 * 7= 32 * 71 
  • Prime factorization of 70 can be expressed as 2 * 5 * 7 = 21 * 51 * 71
  • Prime factorization of 77 can be expressed as 7 * 11 = 71 * 111

So, the LCM of 63, 70, and 77 = 21 * 32 * 51 * 7* 111 = 2 * 3 * 3 * 5 * 7 * 11 = 6930

LCM of 63, 70, and 77 Using the Listing Method

The listing method is one of the methods for finding the LCM. To find the LCM of 63, 70, and 77 using the listing method, follow the following steps:

  • Step 1: Write down the first few multiples of 63, 70, and 77 separately.
  • Step 2: Out of all the multiples of 63, 70, and 77, focus on the multiples that are common to both the numbers, that is, 63, 70, and 77.
  • Step 3: Now, out of all the common multiples, take out the smallest common multiple. That will be the LCM of 63, 70, and 77.

LCM of 63, 70, and 77 can be obtained using the listing method as

  • Multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567, 630,…,6804, 6867, 6930, 6993, 7056,…
  • Multiples of 70 are 70, 140, 210, 280, 350, 420, 490, 560, 630, 700,…,6790, 6860, 6930, 7000, 7070, 7140,…
  • Multiples of 77 are 77, 154, 231, 308, 385, 462, 539, 616, 693, 770,…,6776, 6853, 6930, 7007, 7084, 7161,… 

Here, it is clear that the least common multiple is 6930. So, the LCM of 63, 70, and 77 is 6930.

LCM of 63, 70, and 77 Using the Division Method

The division method is one of the methods for finding the LCM. To find the LCM of 63, 70, and 77 using the division method, divide 63, 70, and 77 by the smallest prime number, which is divisible by any of them. Then, the prime factors further obtained will be used to calculate the final LCM of 63, 70, and 77.

Follow the following steps to find the LCM of 63, 70, and 77 using the division method:

  • Step 1: Write the numbers for which you have to find the LCM, that is 63, 70, and 77 in this case, separated by commas.
  • Step 2: Now, find the smallest prime number, which is divisible by either 63 or 70, or 77.
  • Step 3: If any of the numbers among 63, 70, and 77 are not divisible by the respective prime number, write that number in the next row just below it and proceed further.
  • Step 4: Continue dividing the numbers obtained after each step by the prime numbers, until you get the result as 1 in the entire row.
  • Step 5: Now, multiply all the prime numbers and the final result will be the LCM of 63, 70, and 77.

LCM of 63, 70, and 77 can be obtained using the division method as

Prime FactorsFirst NumberSecond NumberThird Number
2637077
3633577
3213577
573577
77777
111111
 111

So, the LCM of 63, 70, and 77 = 2 * 3 * 3 * 5 * 7 * 11= 6930

What Is the Formula for Finding the LCM of 63, 70, and 77?

LCM of 63, 70, and 77 can be calculated using the formula:

LCM (63, 70, 77) = [(63 * 70 * 77) * HCF (63, 70, 77)] / [HCF (63, 70) * HCF (70, 77) * HCF (63, 77)]
where HCF is the highest common factor or the greatest common divisor.

Problems Based on LCM of 63, 70, and 77

Question 1: If the product of three numbers is 339570, their HCF is 7, and the product of the HCF of the 1st and 2nd number and 2nd and 3rd number, and 1st and 3rd number among three numbers is 343, find the LCM.
Solution:

As we know,
LCM of three numbers = (Product of three numbers * HCF) / [(HCF of 1st and 2nd number) * (HCF of 2nd and 3rd number) * (HCF 1st and 3rd number)]
It is given that,
product of the numbers = 339570, HCF = 7, and the product of the HCF of the 1st and 2nd number and 2nd and 3rd number, and 1st and 3rd number = 343
So, LCM = (339570 * 7) / 343
LCM = 2376990 / 343
LCM = 6930 
Hence, the LCM is 6930.

 

Question 2: What are the other numbers having the LCM as 6930? Show the representation using the prime factorization method.
Solution:

Other than 63, 70, and 77, LCM of 77 and 90 is also 6930. We will prove this using the prime factorization method.
To find the LCM of 63, 70, and 77 using the prime factorization method, first, we will find the prime factors of 63, 70, and 77 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 63, 70, and 77.

  • Prime factorization of 63 can be expressed as 3 * 3 * 7 = 31 * 31 * 7= 32 * 71 
  • Prime factorization of 70 can be expressed as 2 * 5 * 7 = 21 * 51 * 71
  • Prime factorization of 77 can be expressed as 7 * 11 = 71 * 111

So, the LCM of 63, 70, and 77 = 21 * 32 * 51 * 7* 111 = 2 * 3 * 3 * 5 * 7 * 11 = 6930

Now, to find the LCM of 77 and 90 using the prime factorization method, first, we will find the prime factors of 77 and 90 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 77 and 90.

  • Prime factorization of 77 can be expressed as 7 * 11 = 71 * 111
  • Prime factorization of 90 can be expressed as 2 * 3 * 3 * 5 = 21 * 31 * 31 * 5= 21 * 32 * 51 

So, the LCM of 77 and 90 = 21 * 32 * 51 * 7* 111 = 2 * 3 * 3 * 5 * 7 * 11 = 6930

 

Question 3: Find the LCM of 63, 70, and 77 using the division method.
Solution:

To find the LCM of 63, 70, and 77 using the division method, first, we will find the smallest prime number, which is divisible by either 63 or 70 or 77. If any of the numbers among 63, 70, and 77 is not divisible by the respective prime number, we will write that number in the next row just below it and proceed further. We will continue dividing the numbers obtained after each step by the prime numbers until we get the result as 1 in the entire row. We will multiply all the prime numbers and the final result will be the LCM of 63, 70, and 77.

Prime FactorsFirst NumberSecond NumberThird Number
2637077
3633577
3213577
573577
77777
111111
 111

So, the LCM of 63, 70, and 77 = 2 * 3 * 3 * 5 * 7 * 11= 6930

 

Question 4: Find the smallest number divisible by 63, 70, and 77.
Solution:

The smallest number divisible by 63, 70, and 77 is the LCM of 63, 70, and 77.
Using the listing method, we can write the LCM of 63, 70, and 77 as Multiples of 63 are 63, 126, 189, 252, 315, 378, 441, 504, 567, 630,…,6804, 6867, 6930, 6993, 7056,…

  • Multiples of 70 are 70, 140, 210, 280, 350, 420, 490, 560, 630, 700,…,6790, 6860, 6930, 7000, 7070, 7140,…
  • Multiples of 77 are 77, 154, 231, 308, 385, 462, 539, 616, 693, 770,…,6776, 6853, 6930, 7007, 7084, 7161,… 

Here, the smallest number divisible by 63, 70, and 77 is 6930.

 

Question 5: Find the LCM of 63, 70, and 77 using the prime factorization method.
Solution:

To find the LCM of 63, 70, and 775 using the prime factorization method, first, we will find the prime factors of 63, 70, and 77 using the repeated division method. Then, we will write all the prime factors in their exponent forms and multiply the prime factors having the highest power. The final result after multiplication will be the LCM of 63, 70, and 77.

  • Prime factorization of 63 can be expressed as 3 * 3 * 7 = 31 * 31 * 7= 32 * 71 
  • Prime factorization of 70 can be expressed as 2 * 5 * 7 = 21 * 51 * 7
  • Prime factorization of 77 can be expressed as 7 * 11 = 71 * 11

So, the LCM of 63, 70, and 77 = 21 * 32 * 51 * 7* 111 = 2 * 3 * 3 * 5 * 7 * 11 = 6930

 

Frequently Asked Questions (FAQs)

Are the LCM of 63 and 70 the same as the LCM of 70 and 77?
LCM of 63 and 70 is 630 and LCM of 70 and 77 is 770. So, the LCM of 63 and 70 are not the same as the LCM of 70 and 77.

 

What is the LCM of 63, 70, and 77?
LCM of 63, 70, and 77 is 6930.

 

What are the first three common numbers divisible by 63, 70, and 77?
The first three common numbers divisible by 63, 70, and 77 are 6930, 13860, and 20790. 

 

What are the methods to find the LCM of 63, 70, and 77?
There are 3 major methods for finding the LCM of 63, 70, and 77. These methods are:

1. Prime Factorization Method
2. Listing Method  
3. Division Method 

 

Are LCM and HCF of 63, 70, and 77 the same?
LCM of 63, 70, and 77 is 6930, and HCF of 63, 70, and 77 is 7. So, LCM and HCF of 63, 70, and 77 are not the same.

We hope you understand all the basics of how to find the LCM of 67, 70, and 77.

Written by

Prerit Jain

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