LCM of 106 and 264
13992 is the LCM of 106 and 264. 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 106 and 264, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 106 and 264?
lcm (106 264) = (?)
106 => 2 x 53
264 => 2 x 2 x 2 x 3 x 11
= 2 x 53 x 2 x 2 x 3 x 11
= 13992
lcm (106 and 264) = 13992
13992 is the LCM of 106 and 264.
where,
106 is a positive integer,
264 is a positive integer,
13992 is the LCM of 106 and 264,
{2} in {2 x 53, 2 x 2 x 2 x 3 x 11} is the common factors of 106 and 264,
{53 x 2 x 2 x 3 x 11} in {2 x 53, 2 x 2 x 2 x 3 x 11} are the uncommon factors of 106 and 264.
Use in Mathematics: LCM of 106 and 264
The below are some of the mathematical applications where lcm of 106 and 264 can be used:
- to find the least number which is exactly divisible by 106 and 264.
- to find the common denominator for two fractions having 106 and 264 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 106 and 264 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 106 seconds and bell B tolls at 264 seconds repeatedly. The answer is that all bells A and B toll together at 13992 seconds for the first time, at 27984 seconds for the second time, at 41976 seconds for the third time and so on.
Important Notes: 106 and 264 lcm
The below are the important notes to be remembered while solving the lcm of 106 and 264:
- The common prime factors and the remaining prime factors of 106 and 264 should be multiplied to find the least common multiple of 106 and 264, when solving lcm by using prime factors method.
- The results of lcm of 106 and 264, and the lcm of 264 and 106 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 106 and 264?
The below solved example with step by step work shows how to find what is the lcm of 106 and 264 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 106 and 264?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 106
B = 264
What to be found:
find the lcm of 106 and 264
step 2 Find the prime factors of 106 and 264:
Prime factors of 106 = 2 x 53
Prime factors of 264 = 2 x 2 x 2 x 3 x 11
step 3 Identify the repeated and non-repeated prime factors of 106 and 264:
{2} is the most repeated factor and {53 x 2 x 2 x 3 x 11} are the non-repeated factors of 106 and 264.
step 4 Find the product of repeated and non-repeated prime factors of 106 and 264:
= 2 x 53 x 2 x 2 x 3 x 11
= 13992
lcm(106 and 264) = 13992
Hence,
lcm of 106 and 264 is 13992
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 106 and 264.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 106 and 264
What to be found:
lcm (106, 264) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
106 and 264
step 3 Choose the divisor which divides each or most of the given integers (106 and 264), 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 106 and 264 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 106 | 264 |
| 2 | 53 | 132 |
| 2 | 53 | 66 |
| 3 | 53 | 33 |
| 11 | 53 | 11 |
| 53 | 53 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 106 and 264:
= 2 x 2 x 2 x 3 x 11 x 53
= 13992
LCM(106, 264) = 13992
The LCM of two numbers 106 and 264 is 13992