LCM of 18 and 81 is 162. 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 18 and 81, is the smallest number among all the common multiples of 18 and 81.
What is the LCM of 18 and 81?
The Least Common Multiple or Lowest Common Multiple of 18 and 81 is 162.
How to Find LCM of 18 and 81?
Let us see the different methods for finding the LCM of 18 and 81.
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 18 and 81 Using Prime Factorisation Method
Prime factorization of 18 and 81 is (2 × 3 × 3) = 21× 32 and (3 × 3 × 3 × 3) = 34 respectively .
LCM of 18 and 81 can be obtained by multiplying prime factors raised to their respective highest power,
i.e 21 × 34 = 162.
Hence, the LCM of 18 and 81 by prime factorization is 162.
LCM of 18 and 81 by Division Method
To calculate the LCM of 18 and 81 by the division method, we will divide the numbers 18 and 81 by their prime factors. The product of these divisors gives the LCM of 18 and 81.
Let us see the steps to follow:
Step 1: Now let us find the smallest prime number that is a factor of at least one of the numbers, 18 and 81.
Step 2: If any of the given numbers 18 or 81 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 the remainder is in 1’s.
The LCM of 18 and 81 by division method is 162.
| 2 | 18 | 81 |
| 3 | 9 | 81 |
| 3 | 3 | 27 |
| 3 | 1 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
LCM= 2 × 3 × 3 × 3 × 3= 162
LCM of 18 and 81 by Listing Multiples
To Calculate the LCM of 18 and 81, let us list the multiples of 18 and 81
Multiples of 18: 18, 36, 54, 72, 90, …
Multiples of 81: 81, 162, 243, 324, …
Step 1: List out few multiples of 18 and 81 as shown above
Step 2: Now the common multiples from the multiples of 18 and 81 are 162, …
Step 3: The smallest common multiple of 18 and 81 is 162.
Hence the least common multiple of 18 and 81 = 162
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Solved Example
Example:
Find the smallest number that is divisible by 18 and 81 exactly.
Solution:
The smallest number that is divisible by 18 and 81 exactly is their LCM.
Therefore, the LCM of 18 and 81 is 162.
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