LCM of 20 and 30 is equal to 60. The comprehensive work provides more insight of how to find what is the lcm of 20 and 30 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 20 and 30?__

lcm (20 30) = (?)

20 => **2 x 2 x 5**

30 => **2 x 3 x 5**

= 2 x 5 x 2 x 3

= 60

lcm (20 and 30) = 60

**60 is the lcm of 20 and 30.**

__where,__

20 is a positive integer,

30 is a positive integer,

60 is the lcm of 20 and 30,

{2 x 5} in {2 x 2 x 5, 2 x 3 x 5} are the common factors of 20 and 30,

{2 x 3} in {2 x 2 x 5, 2 x 3 x 5} are the uncommon factors of 20 and 30.

__Use in Mathematics: LCM of 20 and 30__

The below are some of the mathematical applications where lcm of 20 and 30 can be used:

- to find the least number which is exactly divisible by 20 and 30.
- to find the common denominator for two fractions having 20 and 30 as denominators in the unlike fractions addition or subtraction.

In the context of lcm real world problems, the lcm of 20 and 30 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 20 seconds and bell B tolls at 30 seconds repeatedly. The answer is that all bells A and B toll together at 60 seconds for the first time, at 120 seconds for the second time, at 180 seconds for the third time and so on.

The below are the important notes to be remembered while solving the lcm of 20 and 30:

- The common prime factors and the remaining prime factors of 20 and 30 should be multiplied to find the least common multiple of 20 and 30, when solving lcm by using prime factors method.
- The results of lcm of 20 and 30, and the lcm of 30 and 20 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.

The below solved example with step by step work shows how to find what is the lcm of 20 and 30 by using prime factors method and division method.

__Solved example using prime factors method:__

What is the LCM of 20 and 30?

step 1
Address the input parameters, values and observe what to be found:

__Input parameters and values:__

A = 20

B = 30

__What to be found:__

find the lcm of 20 and 30

step 2 Find the prime factors of 20 and 30:

Prime factors of 20 = 2 x 2 x 5

Prime factors of 30 = 2 x 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 20 and 30:

{2, 5} are the most repeated factors and {2 x 3} are the non-repeated factors of 20 and 30.

step 4 Find the product of repeated and non-repeated prime factors of 20 and 30:

= 2 x 5 x 2 x 3

= 60

lcm(20 and 30) = 60

Hence,

lcm of 20 and 30 is 60

This special division method is the easiest way to understand the entire calculation of what is the lcm of 20 and 30.

step 1 Address the input parameters, values and observe what to be found:

Integers: 20 and 30

lcm (20, 30) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:

20 and 30

step 3 Choose the divisor which divides each or most of the given integers (20 and 30), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 20 and 30 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 20 | 30 |

2 | 10 | 15 |

3 | 5 | 15 |

5 | 5 | 5 |

1 | 1 |

step 4 Multiply the divisors to find the lcm of 20 and 30:

= 2 x 2 x 3 x 5

= 60

LCM(20, 30) = 60

The least common multiple for two numbers 20 and 30 is 60