LCM of 48 and 120 is 240. 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 48 and 120, is the smallest number among all the common multiples of 48 and 120.
What is the LCM of 48 and 120?
The Least Common Multiple or Lowest Common Multiple of 48 and 120 is 240.
How to Find LCM of 48 and 120?
Let us see the different methods for finding the LCM of 48 and 120
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 48 and 120 Using Prime Factorisation Method
Prime factorization of 48 and 120 is (2 × 2 × 2 × 2 × 3) = 24× 31 and ( 2 × 2 × 2 × 3 × 5 ) = 23 × 31 × 51 respectively.
LCM of 48 and 120 can be obtained by multiplying prime factors raised to their respective highest power,
i.e 24× 31× 51 = 240.
Hence, the LCM of 48 and 120 by prime factorization is 240.
LCM of 48 and 120 by division method
To Calculate the LCM of 48 and 120 by division method, we will divide the numbers 48 and 120 by their prime factors. The product of these divisors gives the LCM of 48 and 120
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, 48 and 120.
Step 2: If any of the given numbers 48 or 120 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 48 and 120 by division method is 240.
|
2 |
48, 120 |
|
2 |
24, 60 |
|
2 |
12, 30 |
|
2 |
6, 15 |
|
3 |
3, 15 |
|
5 |
1, 5 |
| 1, 1 |
LCM= 2 × 2 × 2 × 2 × 3 × 5 = 240
LCM of 48 and 120 by Listing Multiples
To Calculate the LCM of 48 and 120, let us list the multiples of 48 and 120
Multiples of 48: 48, 96, 144, 192, 240, 288…
Multiples of 120: 120, 240, 360…
Step 1: List out a few multiples of 48 and 120
Step 2: Now the common multiples from the multiples of 48 and 120 are 240, 480, …
Step 3: The smallest common multiple of 48 and 120 is 240.
Hence the least common multiple of 48 and 120 = 240
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Solved Example
Example:
Find the smallest number that is divisible by 48 and 120 exactly.
Solution:
The smallest number divisible by 48 and 120 is their LCM.
Therefore, the LCM of 48 and 120 is 240.
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