LCM of 75 and 103
7725 is the LCM of 75 and 103. 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 75 and 103, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 75 and 103?
lcm (75 103) = (?)
75 => 3 x 5 x 5
103 => 103
= 3 x 5 x 5 x 103
= 7725
lcm (75 and 103) = 7725
7725 is the LCM of 75 and 103.
where,
75 is a positive integer,
103 is a positive integer,
7725 is the LCM of 75 and 103,
There is no common factors of 75 and 103 in {3 x 5 x 5, 103},
{3 x 5 x 5 x 103} in {3 x 5 x 5, 103} are the uncommon factors of 75 and 103.
Use in Mathematics: LCM of 75 and 103
The below are some of the mathematical applications where lcm of 75 and 103 can be used:
- to find the least number which is exactly divisible by 75 and 103.
- to find the common denominator for two fractions having 75 and 103 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 75 and 103 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 75 seconds and bell B tolls at 103 seconds repeatedly. The answer is that all bells A and B toll together at 7725 seconds for the first time, at 15450 seconds for the second time, at 23175 seconds for the third time and so on.
Important Notes: 75 and 103 lcm
The below are the important notes to be remembered while solving the lcm of 75 and 103:
- The common prime factors and the remaining prime factors of 75 and 103 should be multiplied to find the least common multiple of 75 and 103, when solving lcm by using prime factors method.
- The results of lcm of 75 and 103, and the lcm of 103 and 75 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 75 and 103?
The below solved example with step by step work shows how to find what is the lcm of 75 and 103 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 75 and 103?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 75
B = 103
What to be found:
find the lcm of 75 and 103
step 2 Find the prime factors of 75 and 103:
Prime factors of 75 = 3 x 5 x 5
Prime factors of 103 = 103
step 3Identify the repeated and non-repeated prime factors of 75 and 103:
Since there is no common factors between 75 and 103, multiplying the given numbers directly provides the LCM of
75 and 103.
= 75 x 103
= 7725
lcm(75 and 103) = 7725
Hence,
lcm of 75 and 103 is 7725
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 75 and 103.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 75 and 103
What to be found:
lcm (75, 103) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
75 and 103
step 3 Choose the divisor which divides each or most of the given integers (75 and 103), 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 75 and 103 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 75 | 103 |
| 5 | 25 | 103 |
| 5 | 5 | 103 |
| 103 | 1 | 103 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 75 and 103:
= 3 x 5 x 5 x 103
= 7725
LCM(75, 103) = 7725
The LCM of two numbers 75 and 103 is 7725