LCM of 6, 7 and 8 is 168. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive number that is a common multiple for the given group of numbers. Here the given set of numbers are 6, 7 and 8. The smallest common multiple for all these numbers among many is 168, and hence it is the LCM. You can refer to LCM with Examples to understand better.
What is LCM of 6, 7 and 8
The Least Common Multiple or Lowest Common Multiple of 6, 7 and 8 is 168.
How to Find LCM of 6, 7 and 8?
LCM of 6, 7 and 8 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6, 7 and 8 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 6, 7 and 8 can be expressed as;
6 = 2 × 3
7 = 1 × 7
8 = 2 × 2 × 2
The product of prime factors of 6, 7 and 8 forms the LCM. Therefore
LCM(6, 7 and 8) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 6, 7 and 8 Using Division Method
In the Division Method, following steps are followed
- Divide the number 6, 7 and 8 by prime numbers starting from the smallest.
- All numbers to be divided till the remainder is 1.
- Multiply the prime divisors to get the LCM.
Division table for 6, 7 and 8 shown below;
LCM(6, 7 and 8) = 2 × 2 × 2 × 3 × 7 = 168
LCM of 6, 7 and 8 Using Listing the Multiples
By listing all the multiples of 6, 7, and 8, we can observe the smallest/least common multiple, which is the LCM. Below is the list of multiples for 6, 7 and 8
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182
Multiples of 8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184
LCM(6, 7 and 8) = 168
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 6, 7 and 8?
Answer: 168 is the smallest number that is divisible by 6, 7 and 8.
What is the LCM of 3 and 168?
Answer: LCM of 3 and 168 is 168.
Frequently Asked Questions on LCM of 6, 7 and 8
Q1
What is the LCM of 6, 7 and 8?
The LCM of 6, 7 and 8 is 168.
Q2
What is the difference between the LCM 6, 7 and 8 and HCF of 6, 7 and 8?
The LCM of 6, 7 and 8 is 168 and HCF of 6, 7 and 8 is 1.
Q3
Is the LCM and LCD both the same for 6, 7 and 8?
Yes. The LCM and Lowest Common Divisor are both the same for 6, 7 and 8 which is 168.
Q4
What are the first 3 common multiples of 6, 7 and 8?
The first three common multiples of 6, 7 and 8 are 168, 336, and 504.
Q5
Is the LCM of 6 and 7 same as the LCM of 7 and 8?
No. LCM of 6 and 7 is 42, whereas the LCM of 7 and 8 is 56. They are not the same.
FAQs
LCM of 6, 7, and 8 by Prime Factorization
What is the LCM of 6 and 8 method? ›
Solved Examples
1 Determine the smallest number that is divisible by 6 and 8 e×actly. Multiples of 6: 6, 12, 18, 24, 30, 36, 42…. Multiples of 8: 8, 16, 24, 32, 40, 48, 56…. Hence the LCM of 6 and 8 is 24.
What is the LCM of 7 and 8 with method? ›
The LCM of 7 and 8 is 56. To find the LCM of 7 and 8, we need to find the multiples of 7 and 8 (multiples of 7 = 7, 14, 21, 28 . . . . 56; multiples of 8 = 8, 16, 24, 32 . . . . 56) and choose the smallest multiple that is exactly divisible by 7 and 8, i.e., 56.
What is the LCM of 6 and 7 and 8 and 9 and 12? ›
6, 7, 8, 9, and 12. Concept used: The least common multiple (LCM) of a set of numbers is the smallest number that leaves 0 as the remainder each time when divided by any of those numbers. So, 504 is the smallest number that leaves 0 as the remainder each time when divided by any of 6, 7, 8, 9, and 12.
What is the LCM of 6 and 7? ›
LCM of 6 and 7 is 42. Among all common multiples of 6 and 7, the LCM of 6 and 7 is the smallest number. (6, 12, 18, 24, 30, 36, and so on) and (7, 14, 21, 28, 35, 42, 49, and so on) are the first few multiples of 6 and 7.
How to calculate LCM? ›
Step 1: Finding each number's prime factorization is the first step in computing the LCM using the prime factors approach. Step 2: When you write each number as a product of primes. Step 3: Now take the highest power of each prime number. Step 4: To obtain the LCM, multiply the prime numbers.
What is the LCM of 6 8 and 8? ›
The LCM of 6 and 8 is 24. To find the least common multiple (LCM) of 6 and 8, we need to find the multiples of 6 and 8 (multiples of 6 = 6, 12, 18, 24; multiples of 8 = 8, 16, 24, 32) and choose the smallest multiple that is exactly divisible by 6 and 8, i.e., 24.
What is the LCM of 6 7 and 8 using prime factorization? ›
LCM of 6, 7, and 8 by Prime Factorization
Prime factorization of 6, 7, and 8 is (2 × 3) = 21 × 31, (7) = 71, and (2 × 2 × 2) = 23 respectively. LCM of 6, 7, and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2. Hence, the LCM of 6, 7, and 8 by prime factorization is 168.
What is the LCM of 7 and 7 and 7? ›
LCM of 7 and 7 is 7. Least Common Multiple or the Lowest Common Multiple is the common multiple for a given set of numbers. Here 7 and 7 is the given set of numbers, and since it is the same number, the common multiple will be 7. The LCM is also known as LCD, Least Common Divisor and for (7, 7) is 7.
What is the LCM 6 8 9 answer? ›
LCM of 6, 8 and 9 is 72. LCM often used for Least Common Multiple or the Lowest common multiple, also known as LCD, Least Common Divisor is the number that is a common multiple to the given set of numbers.
The GCF of 6 and 8 is 2. To calculate the greatest common factor (GCF) of 6 and 8, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 6 and 8, i.e., 2.
What factors do 6 and 8 have in common? ›
There are 2 common factors of 6 and 8, and they are 1 and 2. Therefore, the Highest Common Factor of 6 and 8 is 2.
What is the least number which is divisible by 6 7 8 9 10 12 and leaves remainders 1 in each case? ›
This mean x−1 is common multiple of 6,7,8,9 6 , 7 , 8 , 9 and 12 . The least common multiple of 6,7,8,9 6 , 7 , 8 , 9 and 12 is the least value of x−1 which is 504 . The other multiples are 1008 , 1512 etc. Accordingly, the least value of x is 505.
What is the LCM of 8 7 and 9? ›
What is LCM of 7, 8 and 9. The Least Common Multiple or Lowest Common Multiple of 7, 8 and 9 is 504.
What is the LCM of 6 7 and 9? ›
The smallest number that is divisible by 6, 7 and 9 exactly is their LCM. Therefore, the LCM of 6, 7 and 9 is 126.
What are the common factors of 6 and 8 using any method? ›
There are 2 common factors of 6 and 8, and they are 1 and 2. Therefore, the Highest Common Factor of 6 and 8 is 2.
What is the LCM by common division method 6 8 12? ›
The least common multiple of 6, 8 and 12 is 24. Therefore the smallest number that is divisible by 6, 8, 12 exactly is 24.
What do 6 and 8 have in common? ›
Therefore, common factors of 6 and 8 are 1 and 2.
What is the LCM of 6 8 and 10 by division method? ›
The LCM of 6, 8, and 10 is the product of all prime numbers on the left, i.e. LCM(6, 8, 10) by division method = 2 × 2 × 2 × 3 × 5 = 120.
