LCM of 58 and 60 is equal to 1740. The comprehensive work provides more insight of how to find what is the lcm of 58 and 60 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 58 and 60?__

lcm (58 60) = (?)

58 => **2 x 29**

60 => **2 x 2 x 3 x 5**

= 2 x 29 x 2 x 3 x 5

= 1740

lcm (58 and 60) = 1740

**1740 is the lcm of 58 and 60.**

__where,__

58 is a positive integer,

60 is a positive integer,

1740 is the lcm of 58 and 60,

{2} in {2 x 29, 2 x 2 x 3 x 5} is the common factors of 58 and 60,

{29 x 2 x 3 x 5} in {2 x 29, 2 x 2 x 3 x 5} are the uncommon factors of 58 and 60.

__Use in Mathematics: LCM of 58 and 60__

The below are some of the mathematical applications where lcm of 58 and 60 can be used:

- to find the least number which is exactly divisible by 58 and 60.
- to find the common denominator for two fractions having 58 and 60 as denominators in the unlike fractions addition or subtraction.

In the context of lcm real world problems, the lcm of 58 and 60 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 58 seconds and bell B tolls at 60 seconds repeatedly. The answer is that all bells A and B toll together at 1740 seconds for the first time, at 3480 seconds for the second time, at 5220 seconds for the third time and so on.

The below are the important notes to be remembered while solving the lcm of 58 and 60:

- The common prime factors and the remaining prime factors of 58 and 60 should be multiplied to find the least common multiple of 58 and 60, when solving lcm by using prime factors method.
- The results of lcm of 58 and 60, and the lcm of 60 and 58 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 58 and 60 by using prime factors method and division method.

__Solved example using prime factors method:__

What is the LCM of 58 and 60?

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

__Input parameters and values:__

A = 58

B = 60

__What to be found:__

find the lcm of 58 and 60

step 2 Find the prime factors of 58 and 60:

Prime factors of 58 = 2 x 29

Prime factors of 60 = 2 x 2 x 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 58 and 60:

{2} is the most repeated factor and {29 x 2 x 3 x 5} are the non-repeated factors of 58 and 60.

step 4 Find the product of repeated and non-repeated prime factors of 58 and 60:

= 2 x 29 x 2 x 3 x 5

= 1740

lcm(58 and 60) = 1740

Hence,

lcm of 58 and 60 is 1740

This special division method is the easiest way to understand the entire calculation of what is the lcm of 58 and 60.

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

Integers: 58 and 60

lcm (58, 60) = ?

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

58 and 60

step 3 Choose the divisor which divides each or most of the given integers (58 and 60), 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 58 and 60 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 58 | 60 |

2 | 29 | 30 |

3 | 29 | 15 |

5 | 29 | 5 |

29 | 29 | 1 |

1 | 1 |

step 4 Multiply the divisors to find the lcm of 58 and 60:

= 2 x 2 x 3 x 5 x 29

= 1740

LCM(58, 60) = 1740

The least common multiple for two numbers 58 and 60 is 1740