LCM of 122 and 174
10614 is the LCM of 122 and 174. 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 122 and 174, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 122 and 174?
lcm (122 174) = (?)
122 => 2 x 61
174 => 2 x 3 x 29
= 2 x 61 x 3 x 29
= 10614
lcm (122 and 174) = 10614
10614 is the LCM of 122 and 174.
where,
122 is a positive integer,
174 is a positive integer,
10614 is the LCM of 122 and 174,
{2} in {2 x 61, 2 x 3 x 29} is the common factors of 122 and 174,
{61 x 3 x 29} in {2 x 61, 2 x 3 x 29} are the uncommon factors of 122 and 174.
Use in Mathematics: LCM of 122 and 174
The below are some of the mathematical applications where lcm of 122 and 174 can be used:
- to find the least number which is exactly divisible by 122 and 174.
- to find the common denominator for two fractions having 122 and 174 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 122 and 174 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 122 seconds and bell B tolls at 174 seconds repeatedly. The answer is that all bells A and B toll together at 10614 seconds for the first time, at 21228 seconds for the second time, at 31842 seconds for the third time and so on.
Important Notes: 122 and 174 lcm
The below are the important notes to be remembered while solving the lcm of 122 and 174:
- The common prime factors and the remaining prime factors of 122 and 174 should be multiplied to find the least common multiple of 122 and 174, when solving lcm by using prime factors method.
- The results of lcm of 122 and 174, and the lcm of 174 and 122 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 122 and 174?
The below solved example with step by step work shows how to find what is the lcm of 122 and 174 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 122 and 174?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 122
B = 174
What to be found:
find the lcm of 122 and 174
step 2 Find the prime factors of 122 and 174:
Prime factors of 122 = 2 x 61
Prime factors of 174 = 2 x 3 x 29
step 3 Identify the repeated and non-repeated prime factors of 122 and 174:
{2} is the most repeated factor and {61 x 3 x 29} are the non-repeated factors of 122 and 174.
step 4 Find the product of repeated and non-repeated prime factors of 122 and 174:
= 2 x 61 x 3 x 29
= 10614
lcm(122 and 174) = 10614
Hence,
lcm of 122 and 174 is 10614
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 122 and 174.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 122 and 174
What to be found:
lcm (122, 174) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
122 and 174
step 3 Choose the divisor which divides each or most of the given integers (122 and 174), 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 122 and 174 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 122 | 174 |
| 3 | 61 | 87 |
| 29 | 61 | 29 |
| 61 | 61 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 122 and 174:
= 2 x 3 x 29 x 61
= 10614
LCM(122, 174) = 10614
The LCM of two numbers 122 and 174 is 10614