LCM of 35, 78 and 100
27300 is the LCM of 35, 78 and 100. 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 35, 78 and 100, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 35, 78 and 100?
lcm (35 78 100) = (?)
35 => 5 x 7
78 => 2 x 3 x 13
100 => 2 x 2 x 5 x 5
= 2 x 5 x 7 x 3 x 13 x 2 x 5
= 27300
lcm (35, 78 and 100) = 27300
The LCM of 35, 78 and 100 is 27300
where,
35 is a positive integer,
78 is a positive integer,
27300 is the LCM of 35, 78 and 100,
{2, 5} in {5 x 7, 2 x 3 x 13, 2 x 2 x 5 x 5} are the most repeated factors of 35, 78 and 100,
{7, 3, 13, 2, 5} in {5 x 7, 2 x 3 x 13, 2 x 2 x 5 x 5} are the the other remaining factors of 35, 78 and 100.
Use in Mathematics: LCM of 35, 78 and 100
The below are some of the mathematical applications where lcm of 35, 78 and 100 can be used:
- to find the least number which is exactly divisible by 35, 78 and 100.
- to find the common denominators for the fractions having 35, 78 and 100 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 35, 78 and 100 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 35 seconds, B tolls at 78 seconds and C tolls at 100 seconds repeatedly. The answer is that all bells A, B and C toll together at 27300 seconds for the first time, at 54600 seconds for the second time, at 81900 seconds for the third time and so on.
Important Notes: 35, 78 and 100 lcm
The below are the important notes to be remembered while solving the lcm of 35, 78 and 100:
- The repeated and non-repeated prime factors of 35, 78 and 100 should be multiplied to find the least common multiple of 35, 78 and 100, when solving lcm by using prime factors method.
- The results of lcm of 35, 78 and 100 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 35, 78 and 100?
The below solved example with step by step work shows how to find what is the lcm of 35, 78 and 100 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 35, 78 and 100?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 35
B = 78
C = 100
What to be found:
Find lcm of 35, 78 and 100
step 2 Find the prime factors of 35, 78 and 100:
Prime factors of 35 = 5 x 7
Prime factors of 78 = 2 x 3 x 13
Prime factors of 100 = 2 x 2 x 5 x 5
step 3 Identify the repeated and non-repeated prime factors of 35, 78 and 100:
{2, 5} are the most repeated factors and {7, 3, 13, 2, 5} are the non-repeated factors of 35, 78 and 100.
step 4 Find the product of repeated and non-repeated prime factors of 35, 78 and 100:
= 2 x 5 x 7 x 3 x 13 x 2 x 5
= 27300
LCM(35, 78 and 100) = 27300
Hence,
The Least Common Multiple of 35, 78 and 100 is 27300
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 35, 78 and 100.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 35, 78 and 100
What to be found:
lcm (35, 78, 100) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
35, 78 and 100
step 3 Choose the divisor which divides each or most of the given integers (35, 78 and 100), 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 35, 78 and 100 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 35 | 78 | 100 |
| 2 | 35 | 39 | 50 |
| 3 | 35 | 39 | 25 |
| 5 | 35 | 13 | 25 |
| 5 | 7 | 13 | 5 |
| 7 | 7 | 13 | 1 |
| 13 | 1 | 13 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 35, 78 and 100:
= 2 x 2 x 3 x 5 x 5 x 7 x 13
= 27300
LCM(35, 78, 100) = 27300
The LCM of three numbers 35, 78 and 100 is 27300