LCM of 69 and 154
10626 is the LCM of 69 and 154. 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 154, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 69 and 154?
lcm (69 154) = (?)
69 => 3 x 23
154 => 2 x 7 x 11
= 3 x 23 x 2 x 7 x 11
= 10626
lcm (69 and 154) = 10626
10626 is the LCM of 69 and 154.
where,
69 is a positive integer,
154 is a positive integer,
10626 is the LCM of 69 and 154,
There is no common factors of 69 and 154 in {3 x 23, 2 x 7 x 11},
{3 x 23 x 2 x 7 x 11} in {3 x 23, 2 x 7 x 11} are the uncommon factors of 69 and 154.
Use in Mathematics: LCM of 69 and 154
The below are some of the mathematical applications where lcm of 69 and 154 can be used:
- to find the least number which is exactly divisible by 69 and 154.
- to find the common denominator for two fractions having 69 and 154 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 69 and 154 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 154 seconds repeatedly. The answer is that all bells A and B toll together at 10626 seconds for the first time, at 21252 seconds for the second time, at 31878 seconds for the third time and so on.
Important Notes: 69 and 154 lcm
The below are the important notes to be remembered while solving the lcm of 69 and 154:
- The common prime factors and the remaining prime factors of 69 and 154 should be multiplied to find the least common multiple of 69 and 154, when solving lcm by using prime factors method.
- The results of lcm of 69 and 154, and the lcm of 154 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 154?
The below solved example with step by step work shows how to find what is the lcm of 69 and 154 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 69 and 154?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 69
B = 154
What to be found:
find the lcm of 69 and 154
step 2 Find the prime factors of 69 and 154:
Prime factors of 69 = 3 x 23
Prime factors of 154 = 2 x 7 x 11
step 3Identify the repeated and non-repeated prime factors of 69 and 154:
Since there is no common factors between 69 and 154, multiplying the given numbers directly provides the LCM of
69 and 154.
= 69 x 154
= 10626
lcm(69 and 154) = 10626
Hence,
lcm of 69 and 154 is 10626
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 69 and 154.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 69 and 154
What to be found:
lcm (69, 154) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
69 and 154
step 3 Choose the divisor which divides each or most of the given integers (69 and 154), 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 154 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 69 | 154 |
| 3 | 69 | 77 |
| 7 | 23 | 77 |
| 11 | 23 | 11 |
| 23 | 23 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 69 and 154:
= 2 x 3 x 7 x 11 x 23
= 10626
LCM(69, 154) = 10626
The LCM of two numbers 69 and 154 is 10626