LCM of 72, 76 and 82
56088 is the LCM of 72, 76 and 82. 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, 76 and 82, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 72, 76 and 82?
lcm (72 76 82) = (?)
72 => 2 x 2 x 2 x 3 x 3
76 => 2 x 2 x 19
82 => 2 x 41
= 2 x 2 x 2 x 3 x 3 x 19 x 41
= 56088
lcm (72, 76 and 82) = 56088
The LCM of 72, 76 and 82 is 56088
where,
72 is a positive integer,
76 is a positive integer,
56088 is the LCM of 72, 76 and 82,
{2, 2} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 19, 2 x 41} are the most repeated factors of 72, 76 and 82,
{2, 3, 3, 19, 41} in {2 x 2 x 2 x 3 x 3, 2 x 2 x 19, 2 x 41} are the the other remaining factors of 72, 76 and 82.
Use in Mathematics: LCM of 72, 76 and 82
The below are some of the mathematical applications where lcm of 72, 76 and 82 can be used:
- to find the least number which is exactly divisible by 72, 76 and 82.
- to find the common denominators for the fractions having 72, 76 and 82 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 72, 76 and 82 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 72 seconds, B tolls at 76 seconds and C tolls at 82 seconds repeatedly. The answer is that all bells A, B and C toll together at 56088 seconds for the first time, at 112176 seconds for the second time, at 168264 seconds for the third time and so on.
Important Notes: 72, 76 and 82 lcm
The below are the important notes to be remembered while solving the lcm of 72, 76 and 82:
- The repeated and non-repeated prime factors of 72, 76 and 82 should be multiplied to find the least common multiple of 72, 76 and 82, when solving lcm by using prime factors method.
- The results of lcm of 72, 76 and 82 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is LCM of 72, 76 and 82?
The below solved example with step by step work shows how to find what is the lcm of 72, 76 and 82 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 72, 76 and 82?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 72
B = 76
C = 82
What to be found:
Find lcm of 72, 76 and 82
step 2 Find the prime factors of 72, 76 and 82:
Prime factors of 72 = 2 x 2 x 2 x 3 x 3
Prime factors of 76 = 2 x 2 x 19
Prime factors of 82 = 2 x 41
step 3 Identify the repeated and non-repeated prime factors of 72, 76 and 82:
{2, 2} are the most repeated factors and {2, 3, 3, 19, 41} are the non-repeated factors of 72, 76 and 82.
step 4 Find the product of repeated and non-repeated prime factors of 72, 76 and 82:
= 2 x 2 x 2 x 3 x 3 x 19 x 41
= 56088
LCM(72, 76 and 82) = 56088
Hence,
The Least Common Multiple of 72, 76 and 82 is 56088
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 72, 76 and 82.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 72, 76 and 82
What to be found:
lcm (72, 76, 82) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
72, 76 and 82
step 3 Choose the divisor which divides each or most of the given integers (72, 76 and 82), 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, 76 and 82 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 72 | 76 | 82 |
| 2 | 36 | 38 | 41 |
| 2 | 18 | 19 | 41 |
| 3 | 9 | 19 | 41 |
| 3 | 3 | 19 | 41 |
| 19 | 1 | 19 | 41 |
| 41 | 1 | 1 | 41 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 72, 76 and 82:
= 2 x 2 x 2 x 3 x 3 x 19 x 41
= 56088
LCM(72, 76, 82) = 56088
The LCM of three numbers 72, 76 and 82 is 56088