LCM of 72 and 168
504 is the LCM of 72 and 168. 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 72 and 168, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 72 and 168?
lcm (72 168) = (?)
72 => 2 x 2 x 2 x 3 x 3
168 => 2 x 2 x 2 x 3 x 7
= 2 x 2 x 2 x 3 x 3 x 7
= 504
lcm (72 and 168) = 504
504 is the LCM of 72 and 168.
where,
72 is a positive integer,
168 is a positive integer,
504 is the LCM of 72 and 168,
{2 x 2 x 2 x 3} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 3 x 7} are the common factors of 72 and 168,
{3 x 7} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 2 x 3 x 7} are the uncommon factors of 72 and 168.
Use in Mathematics: LCM of 72 and 168
The below are some of the mathematical applications where lcm of 72 and 168 can be used:
- to find the least number which is exactly divisible by 72 and 168.
- to find the common denominator for two fractions having 72 and 168 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 72 and 168 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 72 seconds and bell B tolls at 168 seconds repeatedly. The answer is that all bells A and B toll together at 504 seconds for the first time, at 1008 seconds for the second time, at 1512 seconds for the third time and so on.
Important Notes: 72 and 168 lcm
The below are the important notes to be remembered while solving the lcm of 72 and 168:
- The common prime factors and the remaining prime factors of 72 and 168 should be multiplied to find the least common multiple of 72 and 168, when solving lcm by using prime factors method.
- The results of lcm of 72 and 168, and the lcm of 168 and 72 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 72 and 168?
The below solved example with step by step work shows how to find what is the lcm of 72 and 168 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 72 and 168?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 72
B = 168
What to be found:
find the lcm of 72 and 168
step 2 Find the prime factors of 72 and 168:
Prime factors of 72 = 2 x 2 x 2 x 3 x 3
Prime factors of 168 = 2 x 2 x 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 72 and 168:
{2, 2, 2, 3} are the most repeated factors and {3 x 7} are the non-repeated factors of 72 and 168.
step 4 Find the product of repeated and non-repeated prime factors of 72 and 168:
= 2 x 2 x 2 x 3 x 3 x 7
= 504
lcm(72 and 168) = 504
Hence,
lcm of 72 and 168 is 504
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 72 and 168.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 72 and 168
What to be found:
lcm (72, 168) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
72 and 168
step 3 Choose the divisor which divides each or most of the given integers (72 and 168), 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 72 and 168 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 72 | 168 |
| 2 | 36 | 84 |
| 2 | 18 | 42 |
| 3 | 9 | 21 |
| 3 | 3 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 72 and 168:
= 2 x 2 x 2 x 3 x 3 x 7
= 504
LCM(72, 168) = 504
The LCM of two numbers 72 and 168 is 504