# 8 and 10 LCM

LCM of 8 and 10 is equal to 40. The comprehensive work provides more insight of how to find what is the lcm of 8 and 10 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

__what is the lcm of 8 and 10?__

lcm (8 10) = (?)

8 => **2 x 2 x 2**

10 => **2 x 5**

= 2 x 2 x 2 x 5

= 40

lcm (8 and 10) = 40

**40 is the lcm of 8 and 10.**

__where,__

8 is a positive integer,

10 is a positive integer,

40 is the lcm of 8 and 10,

{2} in {2 x 2 x 2, 2 x 5} is the common factors of 8 and 10,

{2 x 2 x 5} in {2 x 2 x 2, 2 x 5} are the uncommon factors of 8 and 10.

__Use in Mathematics: LCM of 8 and 10__

The below are some of the mathematical applications where lcm of 8 and 10 can be used:

- to find the least number which is exactly divisible by 8 and 10.
- to find the common denominator for two fractions having 8 and 10 as denominators in the unlike fractions addition or subtraction.

__Use in Real-world Problems: 8 and 10 lcm__In the context of lcm real world problems, the lcm of 8 and 10 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 8 seconds and bell B tolls at 10 seconds repeatedly. The answer is that all bells A and B toll together at 40 seconds for the first time, at 80 seconds for the second time, at 120 seconds for the third time and so on.

__Important Notes: 8 and 10 lcm__The below are the important notes to be remembered while solving the lcm of 8 and 10:

- The common prime factors and the remaining prime factors of 8 and 10 should be multiplied to find the least common multiple of 8 and 10, when solving lcm by using prime factors method.
- The results of lcm of 8 and 10, and the lcm of 10 and 8 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 8 and 10?

The below solved example with step by step work shows how to find what is the lcm of 8 and 10 by using prime factors method and division method.

What is the LCM of 8 and 10?

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

A = 8

B = 10

find the lcm of 8 and 10

step 2 Find the prime factors of 8 and 10:

Prime factors of 8 = 2 x 2 x 2

Prime factors of 10 = 2 x 5

step 3 Identify the repeated and non-repeated prime factors of 8 and 10:

{2} is the most repeated factor and {2 x 2 x 5} are the non-repeated factors of 8 and 10.

step 4 Find the product of repeated and non-repeated prime factors of 8 and 10:

= 2 x 2 x 2 x 5

= 40

lcm(8 and 10) = 40

Hence,

lcm of 8 and 10 is 40

This special division method is the easiest way to understand the entire calculation of what is the lcm of 8 and 10.

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

Integers: 8 and 10

lcm (8, 10) = ?

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

8 and 10

step 3 Choose the divisor which divides each or most of the given integers (8 and 10), 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 8 and 10 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

step 4 Multiply the divisors to find the lcm of 8 and 10:

= 2 x 2 x 2 x 5

= 40

LCM(8, 10) = 40

The least common multiple for two numbers 8 and 10 is 40

__Solved example using prime factors method:__What is the LCM of 8 and 10?

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

__Input parameters and values:__A = 8

B = 10

__What to be found:__find the lcm of 8 and 10

step 2 Find the prime factors of 8 and 10:

Prime factors of 8 = 2 x 2 x 2

Prime factors of 10 = 2 x 5

step 3 Identify the repeated and non-repeated prime factors of 8 and 10:

{2} is the most repeated factor and {2 x 2 x 5} are the non-repeated factors of 8 and 10.

step 4 Find the product of repeated and non-repeated prime factors of 8 and 10:

= 2 x 2 x 2 x 5

= 40

lcm(8 and 10) = 40

Hence,

lcm of 8 and 10 is 40

__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 8 and 10.

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

__Input parameters and values:__

Integers: 8 and 10

__What to be found:__

lcm (8, 10) = ?

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

8 and 10

step 3 Choose the divisor which divides each or most of the given integers (8 and 10), 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 8 and 10 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

2 | 8 | 10 |

2 | 4 | 5 |

2 | 2 | 5 |

5 | 1 | 5 |

1 | 1 |

step 4 Multiply the divisors to find the lcm of 8 and 10:

= 2 x 2 x 2 x 5

= 40

LCM(8, 10) = 40

The least common multiple for two numbers 8 and 10 is 40