LCM of 5, 8 and 15 is 120. 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 5, 8 and 15, is the smallest number among all the common multiples of 5, 8 and 15.
What is the LCM of 5, 8 and 15?
The Least Common Multiple or Lowest Common Multiple of 5, 8 and 15 is 120.
How to Find LCM of 5, 8 and 15?
Let us look at the different methods for finding the LCM of 5, 8 and 15.
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 5, 8 and 15 Using Prime Factorisation Method
Prime factorization of 5, 8 and 15 are (5) =51 and (2 × 2 × 2) = 23 and ( 3 × 5 ) = 31 × 51, respectively.
LCM of 5, 8 and 15 can be obtained by multiplying prime factors raised to their respective highest power.
i.e., 23 × 31 × 51 = 120.
Hence, the LCM of 5, 8 and 15 by prime factorization is 120.
LCM of 5,8 and 15 by division method
To calculate the LCM of 5, 8 and 15 by the division method, we will divide the numbers 5, 8 and 15 by their prime factors. The product of these divisors gives the LCM of 5, 8 and 15.
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, 5, 8 and 15.
Step 2: If any of the given numbers 5, 8 or 15 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 5,8 and 15 by division method is 120.
| 2 | 5 | 8 | 15 |
| 2 | 5 | 4 | 15 |
| 2 | 5 | 2 | 15 |
| 3 | 5 | 1 | 15 |
| 5 | 5 | 1 | 5 |
| 1 | 1 | 1 |
LCM= 2 × 2 × 2 × 3 × 5 = 120
LCM of 5, 8 and 15 by Listing Multiples
To calculate the LCM of 5,8 and 15, first, list the multiples of 5, 8 and 15
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, …
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, …
Multiples of 15: 15, 30, 45, 60, 75, 90, …
Step 1: List out a few multiples of 5, 8 and 15.
Step 2: Now the common multiples from the multiples of 5, 8 and 15 are 120, 240, …
Step 3: The smallest common multiple of 5, 8 and 15 is 120.
Hence the least common multiple of 5,8 and 15 = 120
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Solved Example
Example:
Find the smallest number that is divisible by 5,8 and 15 exactly.
Solution:
The smallest number that is divisible by 5, 8 and 15 exactly is their LCM.
Therefore, the LCM of 5, 8 and 15 is 120.
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