LCM of 6, 10 and 45 is equal to 90. The comprehensive work provides more insight of how to find what is the lcm of 6, 10 and 45 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 6, 10 and 45?__

lcm (6 10 45) = (?)

6 => 2 x 3

10 => 2 x 5

45 => 3 x 3 x 5

= 2 x 3 x 5 x 3

= 90

lcm (6, 10 and 45) = 90

90 is the lcm of 6, 10 and 45.

__where,__

6 is a positive integer,

10 is a positive integer,

90 is the lcm of 6, 10 and 45,

{2, 3, 5} in {2 x 3, 2 x 5, 3 x 3 x 5} are the most repeated factors of 6, 10 and 45,

{3} in {2 x 3, 2 x 5, 3 x 3 x 5} is the other remaining factors of 6, 10 and 45.

__Use in Mathematics: LCM of 6, 10 and 45__

The below are some of the mathematical applications where lcm of 6, 10 and 45 can be used:

- to find the least number which is exactly divisible by 6, 10 and 45.
- to find the common denominators for the fractions having 6, 10 and 45 as denominators in the unlike fractions addition or subtraction.

In the context of lcm real world problems, the lcm of 6, 10 and 45 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 6 seconds, B tolls at 10 seconds and C tolls at 45 seconds repeatedly. The answer is that all bells A, B and C toll together at 90 seconds for the first time, at 180 seconds for the second time, at 270 seconds for the third time and so on.

The below are the important notes to be remembered while solving the lcm of 6, 10 and 45:

- The repeated and non-repeated prime factors of 6, 10 and 45 should be multiplied to find the least common multiple of 6, 10 and 45, when solving lcm by using prime factors method.
- The results of lcm of 6, 10 and 45 is identical even if we change the order of given numbers in the lcm calculation, 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 6, 10 and 45 by using either prime factors method and special division method.

__Solved example using prime factors method:__

What is the LCM of 6, 10 and 45?

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

__Input parameters and values:__

A = 6

B = 10

C = 45

__What to be found:__

find the lcm of 6, 10 and 45

step 2 Find the prime factors of 6, 10 and 45:

Prime factors of 6 = 2 x 3

Prime factors of 10 = 2 x 5

Prime factors of 45 = 3 x 3 x 5

step 3 Identify the repeated and non-repeated prime factors of 6, 10 and 45:

{2, 3, 5} are the most repeated factors and {3} is the non-repeated factors of 6, 10 and 45.

step 4 Find the product of repeated and non-repeated prime factors of 6, 10 and 45:

= 2 x 3 x 5 x 3

= 90

lcm(20 and 30) = 90

Hence,

lcm of 6, 10 and 45 is 90

This special division method is the easiest way to understand the entire calculation of what is the lcm of 6, 10 and 45.

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

Integers: 6, 10 and 45

lcm (6, 10, 45) = ?

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

6, 10 and 45

step 3 Choose the divisor which divides each or most of the given integers (6, 10 and 45), 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 6, 10 and 45 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 6 | 10 | 45 |

3 | 3 | 5 | 45 |

3 | 1 | 5 | 15 |

5 | 1 | 5 | 5 |

1 | 1 | 1 |

step 4 Multiply the divisors to find the lcm of 6, 10 and 45:

= 2 x 3 x 3 x 5

= 90

LCM(6, 10, 45) = 90

The least common multiple for three numbers 6, 10 and 45 is 90