LCM of 38 and 45
1710 is the LCM of 38 and 45. 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 38 and 45, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 38 and 45?
lcm (38 45) = (?)
38 => 2 x 19
45 => 3 x 3 x 5
= 2 x 19 x 3 x 3 x 5
= 1710
lcm (38 and 45) = 1710
1710 is the LCM of 38 and 45.
where,
38 is a positive integer,
45 is a positive integer,
1710 is the LCM of 38 and 45,
There is no common factors of 38 and 45 in {2 x 19, 3 x 3 x 5},
{2 x 19 x 3 x 3 x 5} in {2 x 19, 3 x 3 x 5} are the uncommon factors of 38 and 45.
Use in Mathematics: LCM of 38 and 45
The below are some of the mathematical applications where lcm of 38 and 45 can be used:
- to find the least number which is exactly divisible by 38 and 45.
- to find the common denominator for two fractions having 38 and 45 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 38 and 45 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 38 seconds and bell B tolls at 45 seconds repeatedly. The answer is that all bells A and B toll together at 1710 seconds for the first time, at 3420 seconds for the second time, at 5130 seconds for the third time and so on.
Important Notes: 38 and 45 lcm
The below are the important notes to be remembered while solving the lcm of 38 and 45:
- The common prime factors and the remaining prime factors of 38 and 45 should be multiplied to find the least common multiple of 38 and 45, when solving lcm by using prime factors method.
- The results of lcm of 38 and 45, and the lcm of 45 and 38 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 38 and 45?
The below solved example with step by step work shows how to find what is the lcm of 38 and 45 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 38 and 45?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 38
B = 45
What to be found:
find the lcm of 38 and 45
step 2 Find the prime factors of 38 and 45:
Prime factors of 38 = 2 x 19
Prime factors of 45 = 3 x 3 x 5
step 3Identify the repeated and non-repeated prime factors of 38 and 45:
Since there is no common factors between 38 and 45, multiplying the given numbers directly provides the LCM of
38 and 45.
= 38 x 45
= 1710
lcm(38 and 45) = 1710
Hence,
lcm of 38 and 45 is 1710
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 38 and 45.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 38 and 45
What to be found:
lcm (38, 45) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
38 and 45
step 3 Choose the divisor which divides each or most of the given integers (38 and 45), 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 38 and 45 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 38 | 45 |
| 3 | 19 | 45 |
| 3 | 19 | 15 |
| 5 | 19 | 5 |
| 19 | 19 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 38 and 45:
= 2 x 3 x 3 x 5 x 19
= 1710
LCM(38, 45) = 1710
The LCM of two numbers 38 and 45 is 1710