# 90 and 120 LCM

LCM of 90 and 120 is equal to 360. The comprehensive work provides more insight of how to find what is the lcm of 90 and 120 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 90 and 120?__

lcm (90 120) = (?)

90 => **2 x 3 x 3 x 5**

120 => **2 x 2 x 2 x 3 x 5**

= 2 x 3 x 5 x 3 x 2 x 2

= 360

lcm (90 and 120) = 360

**360 is the lcm of 90 and 120.**

__where,__

90 is a positive integer,

120 is a positive integer,

360 is the lcm of 90 and 120,

{2 x 3 x 5} in {2 x 3 x 3 x 5, 2 x 2 x 2 x 3 x 5} are the common factors of 90 and 120,

{3 x 2 x 2} in {2 x 3 x 3 x 5, 2 x 2 x 2 x 3 x 5} are the uncommon factors of 90 and 120.

__Use in Mathematics: LCM of 90 and 120__

The below are some of the mathematical applications where lcm of 90 and 120 can be used:

- to find the least number which is exactly divisible by 90 and 120.
- to find the common denominator for two fractions having 90 and 120 as denominators in the unlike fractions addition or subtraction.

__Use in Real-world Problems: 90 and 120 lcm__In the context of lcm real world problems, the lcm of 90 and 120 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 90 seconds and bell B tolls at 120 seconds repeatedly. The answer is that all bells A and B toll together at 360 seconds for the first time, at 720 seconds for the second time, at 1080 seconds for the third time and so on.

__Important Notes: 90 and 120 lcm__The below are the important notes to be remembered while solving the lcm of 90 and 120:

- The common prime factors and the remaining prime factors of 90 and 120 should be multiplied to find the least common multiple of 90 and 120, when solving lcm by using prime factors method.
- The results of lcm of 90 and 120, and the lcm of 120 and 90 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.

## How-to: What is the LCM of 90 and 120?

__Solved example using prime factors method:__

What is the LCM of 90 and 120?

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

__Input parameters and values:__

A = 90

B = 120

__What to be found:__

find the lcm of 90 and 120

step 2 Find the prime factors of 90 and 120:

Prime factors of 90 = 2 x 3 x 3 x 5

Prime factors of 120 = 2 x 2 x 2 x 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 90 and 120:

{2, 3, 5} are the most repeated factors and {3 x 2 x 2} are the non-repeated factors of 90 and 120.

step 4 Find the product of repeated and non-repeated prime factors of 90 and 120:

= 2 x 3 x 5 x 3 x 2 x 2

= 360

lcm(90 and 120) = 360

Hence,

lcm of 90 and 120 is 360

__Solved example using special division method:__

This special division method is the easiest way to understand the entire calculation of what is the lcm of 90 and 120.

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

__Input parameters and values:__

Integers: 90 and 120

__What to be found:__

lcm (90, 120) = ?

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

90 and 120

step 3 Choose the divisor which divides each or most of the given integers (90 and 120), 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 90 and 120 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 90 | 120 |

2 | 45 | 60 |

2 | 45 | 30 |

3 | 45 | 15 |

3 | 15 | 5 |

5 | 5 | 5 |

1 | 1 |

step 4 Multiply the divisors to find the lcm of 90 and 120:

= 2 x 2 x 2 x 3 x 3 x 5

= 360

LCM(90, 120) = 360

The least common multiple for two numbers 90 and 120 is 360