LCM of 105 and 195 is 1365. The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 105 and 195, 1365 is the first(least or smallest) number that is common in the set of multiples of 105 and 195. The LCM is also known as LCD, Least Common Divisor for 105 and 195 is 1365. You can refer to LCM with Examples for more understanding.
What is LCM of 105 and 195
The Least Common Multiple or Lowest Common Multiple of 105 and 195 is 1365.
How to Find LCM of 105 and 195?
LCM of 105 and 195 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 105 and 195 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 105 and 195 can be expressed as;
105 = 3 x 5 x 7
195 = 3 x 5 x 13
LCM (105, 195) = 3 x 5 x 7 x 13 = 1365
LCM of 105 and 195 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
3 |
105 |
195 |
|
5 |
35 |
65 |
|
7 |
7 |
13 |
|
13 |
1 |
13 |
|
x |
1 |
1 |
Therefore, LCM (105, 195) = 3 x 5 x 7 x 13 = 1365
LCM of 105 and 195 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 105 and 195
Multiples of 105:
105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680 …
Multiples of 195:
195, 390, 585, 780, 975, 1170, 1365, 1560, 1755, 1950 …
LCM (105, 195) = 1365
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 105 and 195?
Answer: 1365 is the smallest number that is divisible by both 105 and 195.
What is the LCM for 5, 105 and 195?
Answer: LCM for 5, 105 and 195 is 1365.
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