LCM of 30 and 48 is 240.The Least Common Divisor, or Least Common Multiple or Lowest common multiple simply known as LCM is the smallest positive integer that is divisible by the given numbers. In the given set of numbers 30 and 48, 240 is the first(least or smallest) number that is common in the set of multiples of 30 and 48. You can use the LCM with Examples to find details on LCM.
What is LCM of 30 and 48
The Least Common Multiple or Lowest Common Multiple of 30 and 48 is 240.
How to Find LCM of 30 and 48?
LCM of 30 and 48 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 48 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 30 and 48 can be expressed as;
30 = 2 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
2 × 3 are the common factors of 30 and 48. The other factors of these two numbers are multiplied to get the LCM.
LCM (30, 48) = 2 × 2 × 2 × 2 × 3 × 5 = 240
LCM of 30 and 48 Using Division Method
In the Division Method, the given set of numbers 30 and 48 are divided by common factors and then uncommon factors together. Product of these common and uncommon prime divisors forms the LCM.
|
2 |
30 |
48 |
|
2 |
15 |
24 |
|
2 |
15 |
12 |
|
2 |
15 |
6 |
|
3 |
15 |
3 |
|
5 |
5 |
1 |
|
× |
1 |
1 |
LCM (30, 48) = 2 × 2 × 2 × 2 × 3 × 5 = 240
LCM of 30 and 48 Using Listing the Multiples
By listing all the multiples of 30 and 48, we can identify the smallest common multiple, which is the LCM. Below is the list of multiples for 30 and 48:
|
Multiples of 30 |
Multiples of 48 |
|
30 |
48 |
|
60 |
96 |
|
90 |
144 |
|
120 |
192 |
|
150 |
240 |
|
180 |
288 |
|
210 |
336 |
|
240 |
384 |
|
270 |
432 |
LCM (30, 48) = 240
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 30 and 48?
Answer: 240 is the smallest number that is divisible by both 30 and 48.
What is the LCM for 2, 3, 30 and 48?
Answer: LCM for 2, 3, 30 and 48 is 240.
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