LCM of 189 and 334
63126 is the LCM of 189 and 334. 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 189 and 334, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 189 and 334?
lcm (189 334) = (?)
189 => 3 x 3 x 3 x 7
334 => 2 x 167
= 3 x 3 x 3 x 7 x 2 x 167
= 63126
lcm (189 and 334) = 63126
63126 is the LCM of 189 and 334.
where,
189 is a positive integer,
334 is a positive integer,
63126 is the LCM of 189 and 334,
There is no common factors of 189 and 334 in {3 x 3 x 3 x 7, 2 x 167},
{3 x 3 x 3 x 7 x 2 x 167} in {3 x 3 x 3 x 7, 2 x 167} are the uncommon factors of 189 and 334.
Use in Mathematics: LCM of 189 and 334
The below are some of the mathematical applications where lcm of 189 and 334 can be used:
- to find the least number which is exactly divisible by 189 and 334.
- to find the common denominator for two fractions having 189 and 334 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 189 and 334 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 189 seconds and bell B tolls at 334 seconds repeatedly. The answer is that all bells A and B toll together at 63126 seconds for the first time, at 126252 seconds for the second time, at 189378 seconds for the third time and so on.
Important Notes: 189 and 334 lcm
The below are the important notes to be remembered while solving the lcm of 189 and 334:
- The common prime factors and the remaining prime factors of 189 and 334 should be multiplied to find the least common multiple of 189 and 334, when solving lcm by using prime factors method.
- The results of lcm of 189 and 334, and the lcm of 334 and 189 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 189 and 334?
The below solved example with step by step work shows how to find what is the lcm of 189 and 334 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 189 and 334?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 189
B = 334
What to be found:
find the lcm of 189 and 334
step 2 Find the prime factors of 189 and 334:
Prime factors of 189 = 3 x 3 x 3 x 7
Prime factors of 334 = 2 x 167
step 3Identify the repeated and non-repeated prime factors of 189 and 334:
Since there is no common factors between 189 and 334, multiplying the given numbers directly provides the LCM of
189 and 334.
= 189 x 334
= 63126
lcm(189 and 334) = 63126
Hence,
lcm of 189 and 334 is 63126
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 189 and 334.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 189 and 334
What to be found:
lcm (189, 334) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
189 and 334
step 3 Choose the divisor which divides each or most of the given integers (189 and 334), 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 189 and 334 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 189 | 334 |
| 3 | 189 | 167 |
| 3 | 63 | 167 |
| 3 | 21 | 167 |
| 7 | 7 | 167 |
| 167 | 1 | 167 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 189 and 334:
= 2 x 3 x 3 x 3 x 7 x 167
= 63126
LCM(189, 334) = 63126
The LCM of two numbers 189 and 334 is 63126