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135 LearnersLast updated on November 29th, 2024
LCM of 6,7 and 8
LCM is a common multiple, the smallest value between the numbers 6,7 and 8. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.
What is the LCM of 6,7 and 8?
The LCM of 6,7 and 8 is 168. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.
LCM of 6,7 and 8 Using Listing the Multiples
Step 1: Write down the multiples of the numbers. Don’t stop too early.
Multiples of 6 = 6,12,18,24,30,36,42,48,54,60,66,72,78,….168
Multiples of 7 = 7,14,21,28,35,42,49,56,…168
Multiples of 8 = 8, 16,24,32,40,48,56,…..168
Step 2: Find the smallest number common between the written multiples of 6,7 and 8
The smallest common multiple is 168
Thus, LCM(6,7,8) = 168
LCM of 6,7 and 8 Using Prime Factorization
Step 1:factorize the numbers into its prime factors
6 = 2×3
7 = 7
8 = 2×2×2
Step 2:find the highest powers of the factors of 6,7 and 8
Step 3:Multiply the highest powers
LCM(6,7,8) = 168
LCM of 6,7 and 8 Using Division Method
- Write the numbers 6,7,8 in a row
- Divide them by their common prime factors, if there is one
- Carry forward the numbers that are left undivided by the previously chosen factor
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (6,7,8) = 168
Common Mistakes and how to avoid them while finding the LCM of 6,7 and 8
LCM of 6,7 and 8, examples
Problem 1
Use the relationship LCM(a,b)×GCF(a,b)=a×b to verify that the LCM of 6 and 8 is 24.
Explanation
Problem 2
Goods are received by a shipping company every 6,7 and 8 months. If the shipments have been received today, when will they next arrive at, the same day?
Explanation
Problem 3
One of the numbers in the LCM calculation of 6, 7, and 8 was incorrectly identified as 4 instead of its correct value. The result was 84 instead of 168. What was the incorrect number?
Explanation
FAQs on LCM of 6,7 and 8
1.List the multiples of 6,7 and 8.
2. How to find LCM in permutation?
3. What is the LCM of 7and 5?
4.What is the LCM of 4,5 and 7?
5.What is the LCM of 4,7 and 10?
Important glossaries for the LCM of 6,7 and 8
- Multiple — product of a number and a natural integer
- Prime factor — number one gets after prime factorization any given number
- Prime factorization — the process of breaking the number into its prime factors
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
