LCM of 105 and 195

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.

lcm of 105 and 195

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.

Frequently Asked Questions on LCM of 105 and 195

Q1

What is the LCM of 105 and 195?

The LCM of 105 and 195 is 1365.
Q2

Is the LCM of 105 and 195 the same as the HCF of 105 and 195?

No. LCM of 105 and 195 is 1365 and the Highest Common Factor of 105 and 195 is 15.
Q3

What are the common factors of 105 and 195?

1, 3 and 5 are the common factors of 105 and 195.

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