LCM of 69 and 178
12282 is the LCM of 69 and 178. 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 69 and 178, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 69 and 178?
lcm (69 178) = (?)
69 => 3 x 23
178 => 2 x 89
= 3 x 23 x 2 x 89
= 12282
lcm (69 and 178) = 12282
12282 is the LCM of 69 and 178.
where,
69 is a positive integer,
178 is a positive integer,
12282 is the LCM of 69 and 178,
There is no common factors of 69 and 178 in {3 x 23, 2 x 89},
{3 x 23 x 2 x 89} in {3 x 23, 2 x 89} are the uncommon factors of 69 and 178.
Use in Mathematics: LCM of 69 and 178
The below are some of the mathematical applications where lcm of 69 and 178 can be used:
- to find the least number which is exactly divisible by 69 and 178.
- to find the common denominator for two fractions having 69 and 178 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 69 and 178 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 69 seconds and bell B tolls at 178 seconds repeatedly. The answer is that all bells A and B toll together at 12282 seconds for the first time, at 24564 seconds for the second time, at 36846 seconds for the third time and so on.
Important Notes: 69 and 178 lcm
The below are the important notes to be remembered while solving the lcm of 69 and 178:
- The common prime factors and the remaining prime factors of 69 and 178 should be multiplied to find the least common multiple of 69 and 178, when solving lcm by using prime factors method.
- The results of lcm of 69 and 178, and the lcm of 178 and 69 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 69 and 178?
The below solved example with step by step work shows how to find what is the lcm of 69 and 178 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 69 and 178?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 69
B = 178
What to be found:
find the lcm of 69 and 178
step 2 Find the prime factors of 69 and 178:
Prime factors of 69 = 3 x 23
Prime factors of 178 = 2 x 89
step 3Identify the repeated and non-repeated prime factors of 69 and 178:
Since there is no common factors between 69 and 178, multiplying the given numbers directly provides the LCM of
69 and 178.
= 69 x 178
= 12282
lcm(69 and 178) = 12282
Hence,
lcm of 69 and 178 is 12282
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 69 and 178.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 69 and 178
What to be found:
lcm (69, 178) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
69 and 178
step 3 Choose the divisor which divides each or most of the given integers (69 and 178), 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 69 and 178 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 69 | 178 |
| 3 | 69 | 89 |
| 23 | 23 | 89 |
| 89 | 1 | 89 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 69 and 178:
= 2 x 3 x 23 x 89
= 12282
LCM(69, 178) = 12282
The LCM of two numbers 69 and 178 is 12282