LCM of 155 and 189
29295 is the LCM of 155 and 189. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 155 and 189, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 155 and 189?
lcm (155 189) = (?)
155 => 5 x 31
189 => 3 x 3 x 3 x 7
= 5 x 31 x 3 x 3 x 3 x 7
= 29295
lcm (155 and 189) = 29295
29295 is the LCM of 155 and 189.
where,
155 is a positive integer,
189 is a positive integer,
29295 is the LCM of 155 and 189,
There is no common factors of 155 and 189 in {5 x 31, 3 x 3 x 3 x 7},
{5 x 31 x 3 x 3 x 3 x 7} in {5 x 31, 3 x 3 x 3 x 7} are the uncommon factors of 155 and 189.
Use in Mathematics: LCM of 155 and 189
The below are some of the mathematical applications where lcm of 155 and 189 can be used:
- to find the least number which is exactly divisible by 155 and 189.
- to find the common denominator for two fractions having 155 and 189 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 155 and 189 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 155 seconds and bell B tolls at 189 seconds repeatedly. The answer is that all bells A and B toll together at 29295 seconds for the first time, at 58590 seconds for the second time, at 87885 seconds for the third time and so on.
Important Notes: 155 and 189 lcm
The below are the important notes to be remembered while solving the lcm of 155 and 189:
- The common prime factors and the remaining prime factors of 155 and 189 should be multiplied to find the least common multiple of 155 and 189, when solving lcm by using prime factors method.
- The results of lcm of 155 and 189, and the lcm of 189 and 155 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 155 and 189?
The below solved example with step by step work shows how to find what is the lcm of 155 and 189 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 155 and 189?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 155
B = 189
What to be found:
find the lcm of 155 and 189
step 2 Find the prime factors of 155 and 189:
Prime factors of 155 = 5 x 31
Prime factors of 189 = 3 x 3 x 3 x 7
step 3Identify the repeated and non-repeated prime factors of 155 and 189:
Since there is no common factors between 155 and 189, multiplying the given numbers directly provides the LCM of
155 and 189.
= 155 x 189
= 29295
lcm(155 and 189) = 29295
Hence,
lcm of 155 and 189 is 29295
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 155 and 189.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 155 and 189
What to be found:
lcm (155, 189) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
155 and 189
step 3 Choose the divisor which divides each or most of the given integers (155 and 189), 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 155 and 189 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 155 | 189 |
| 3 | 155 | 63 |
| 3 | 155 | 21 |
| 5 | 155 | 7 |
| 7 | 31 | 7 |
| 31 | 31 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 155 and 189:
= 3 x 3 x 3 x 5 x 7 x 31
= 29295
LCM(155, 189) = 29295
The LCM of two numbers 155 and 189 is 29295