LCM of 4, 7 and 8 is 56. LCM is abbreviated as Least Common multiple or Lowest common multiple. LCM is the simplest method to find out the smallest common multiples between two or more than two numbers.
The LCM of 4, 7 and 8 is the result of multiplying all prime factors, the greatest number of times they occur in either number.
What is the LCM of 4, 7 and 8?
The Least Common Multiple or Lowest Common Multiple of 4,7 and 8 is 56.
How to Find LCM of 4, 7 and 8?
Let us look at the different methods for finding the LCM of 4, 7 and 8
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 4, 7 and 8 Using Prime Factorisation Method
Prime factorization of 4, 7 and 8 is:
4 = 2 × 2 = 22
7 = 71
8 = 2 × 2 × 2 = 23 , respectively.
LCM of 4,7 and 8 can be obtained by multiplying prime factors raised to their respective highest powers.
Hence, the LCM of 4, 7 and 8 by prime factorization is 56.
LCM of 4, 7 and 8 by Division Method
To calculate the LCM of 4,7 and 8 by division method, we will divide the numbers 4, 7 and 8 by their prime factors. The product of these divisors gives the LCM of 4,7 and 8.
Let us see the steps to follow:
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4, 7 and 8. Write down the prime number 2 on the left as shown in the table below.
Step 2: If any of the given numbers 4 or 7 or 8 is a multiple of 2, divide it by 2 and write the quotient below it. Bring down the number as it is, if it is not divisible by the prime number.
Step 3: Continue these steps until you get only 1’s in the last row.
The LCM of 4,7 and 8 by division method is 56.
| 2 | 4 | 7 | 8 |
| 2 | 2 | 7 | 4 |
| 2 | 1 | 7 | 2 |
| 7 | 1 | 7 | 1 |
| 1 | 1 | 1 |
LCM = 2 × 2 × 2 × 7 =56
LCM of 4,7 and 8 by Listing Multiples
First to find the LCM of 4, 7 and 8, let us list the multiples of 4, 7 and 8.
Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, …
Multiples of 7 : 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, …
Multiples of 8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, …
Step 1: List out a few multiples of 4, 7 and 8.
Step 2: Now the common multiples from the multiples of 4, 7 and 8 are 56, …
Step 3: The smallest common multiple of 4, 7 and 8 is 56.
Hence the least common multiple of 4,7 and 8 = 56.
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Solved Example
Example:
Find the smallest number that is divisible by 4, 7 and 8 exactly.
Solution:
The smallest number that is divisible by 4, 7 and 8 exactly is their LCM.
Therefore, the LCM of 4, 7 and 8 is 56
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