LCM of 45 and 185
1665 is the LCM of 45 and 185. 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 45 and 185, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 45 and 185?
lcm (45 185) = (?)
45 => 3 x 3 x 5
185 => 5 x 37
= 5 x 3 x 3 x 37
= 1665
lcm (45 and 185) = 1665
1665 is the LCM of 45 and 185.
where,
45 is a positive integer,
185 is a positive integer,
1665 is the LCM of 45 and 185,
{5} in {3 x 3 x 5, 5 x 37} is the common factors of 45 and 185,
{3 x 3 x 37} in {3 x 3 x 5, 5 x 37} are the uncommon factors of 45 and 185.
Use in Mathematics: LCM of 45 and 185
The below are some of the mathematical applications where lcm of 45 and 185 can be used:
- to find the least number which is exactly divisible by 45 and 185.
- to find the common denominator for two fractions having 45 and 185 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 45 and 185 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 45 seconds and bell B tolls at 185 seconds repeatedly. The answer is that all bells A and B toll together at 1665 seconds for the first time, at 3330 seconds for the second time, at 4995 seconds for the third time and so on.
Important Notes: 45 and 185 lcm
The below are the important notes to be remembered while solving the lcm of 45 and 185:
- The common prime factors and the remaining prime factors of 45 and 185 should be multiplied to find the least common multiple of 45 and 185, when solving lcm by using prime factors method.
- The results of lcm of 45 and 185, and the lcm of 185 and 45 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 45 and 185?
The below solved example with step by step work shows how to find what is the lcm of 45 and 185 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 45 and 185?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 45
B = 185
What to be found:
find the lcm of 45 and 185
step 2 Find the prime factors of 45 and 185:
Prime factors of 45 = 3 x 3 x 5
Prime factors of 185 = 5 x 37
step 3 Identify the repeated and non-repeated prime factors of 45 and 185:
{5} is the most repeated factor and {3 x 3 x 37} are the non-repeated factors of 45 and 185.
step 4 Find the product of repeated and non-repeated prime factors of 45 and 185:
= 5 x 3 x 3 x 37
= 1665
lcm(45 and 185) = 1665
Hence,
lcm of 45 and 185 is 1665
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 45 and 185.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 45 and 185
What to be found:
lcm (45, 185) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
45 and 185
step 3 Choose the divisor which divides each or most of the given integers (45 and 185), 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 45 and 185 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 45 | 185 |
| 3 | 15 | 185 |
| 5 | 5 | 185 |
| 37 | 1 | 37 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 45 and 185:
= 3 x 3 x 5 x 37
= 1665
LCM(45, 185) = 1665
The LCM of two numbers 45 and 185 is 1665