LCM of 90, 92 and 95
78660 is the LCM of 90, 92 and 95. 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 90, 92 and 95, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 90, 92 and 95?
lcm (90 92 95) = (?)
90 => 2 x 3 x 3 x 5
92 => 2 x 2 x 23
95 => 5 x 19
= 2 x 5 x 3 x 3 x 2 x 23 x 19
= 78660
lcm (90, 92 and 95) = 78660
The LCM of 90, 92 and 95 is 78660
where,
90 is a positive integer,
92 is a positive integer,
78660 is the LCM of 90, 92 and 95,
{2, 5} in {2 x 3 x 3 x 5, 2 x 2 x 23, 5 x 19} are the most repeated factors of 90, 92 and 95,
{3, 3, 2, 23, 19} in {2 x 3 x 3 x 5, 2 x 2 x 23, 5 x 19} are the the other remaining factors of 90, 92 and 95.
Use in Mathematics: LCM of 90, 92 and 95
The below are some of the mathematical applications where lcm of 90, 92 and 95 can be used:
- to find the least number which is exactly divisible by 90, 92 and 95.
- to find the common denominators for the fractions having 90, 92 and 95 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 90, 92 and 95 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 90 seconds, B tolls at 92 seconds and C tolls at 95 seconds repeatedly. The answer is that all bells A, B and C toll together at 78660 seconds for the first time, at 157320 seconds for the second time, at 235980 seconds for the third time and so on.
Important Notes: 90, 92 and 95 lcm
The below are the important notes to be remembered while solving the lcm of 90, 92 and 95:
- The repeated and non-repeated prime factors of 90, 92 and 95 should be multiplied to find the least common multiple of 90, 92 and 95, when solving lcm by using prime factors method.
- The results of lcm of 90, 92 and 95 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 90, 92 and 95?
The below solved example with step by step work shows how to find what is the lcm of 90, 92 and 95 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 90, 92 and 95?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 90
B = 92
C = 95
What to be found:
Find lcm of 90, 92 and 95
step 2 Find the prime factors of 90, 92 and 95:
Prime factors of 90 = 2 x 3 x 3 x 5
Prime factors of 92 = 2 x 2 x 23
Prime factors of 95 = 5 x 19
step 3 Identify the repeated and non-repeated prime factors of 90, 92 and 95:
{2, 5} are the most repeated factors and {3, 3, 2, 23, 19} are the non-repeated factors of 90, 92 and 95.
step 4 Find the product of repeated and non-repeated prime factors of 90, 92 and 95:
= 2 x 5 x 3 x 3 x 2 x 23 x 19
= 78660
LCM(90, 92 and 95) = 78660
Hence,
The Least Common Multiple of 90, 92 and 95 is 78660
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 90, 92 and 95.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 90, 92 and 95
What to be found:
lcm (90, 92, 95) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
90, 92 and 95
step 3 Choose the divisor which divides each or most of the given integers (90, 92 and 95), 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 90, 92 and 95 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 90 | 92 | 95 |
| 2 | 45 | 46 | 95 |
| 3 | 45 | 23 | 95 |
| 3 | 15 | 23 | 95 |
| 5 | 5 | 23 | 95 |
| 19 | 1 | 23 | 19 |
| 23 | 1 | 23 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 90, 92 and 95:
= 2 x 2 x 3 x 3 x 5 x 19 x 23
= 78660
LCM(90, 92, 95) = 78660
The LCM of three numbers 90, 92 and 95 is 78660