LCM of 15 and 5
15 is the LCM of 15 and 5. 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 15 and 5, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 15 and 5?
lcm (15 5) = (?)
15 => 3 x 5
5 => 5
= 5 x 3
= 15
lcm (15 and 5) = 15
15 is the LCM of 15 and 5.
where,
15 is a positive integer,
5 is a positive integer,
15 is the LCM of 15 and 5,
{5} in {3 x 5, 5} is the common factors of 15 and 5,
{3} in {3 x 5, 5} is the uncommon factors of 15 and 5.
Use in Mathematics: LCM of 15 and 5
The below are some of the mathematical applications where lcm of 15 and 5 can be used:
- to find the least number which is exactly divisible by 15 and 5.
- to find the common denominator for two fractions having 15 and 5 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 15 and 5 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 15 seconds and bell B tolls at 5 seconds repeatedly. The answer is that all bells A and B toll together at 15 seconds for the first time, at 30 seconds for the second time, at 45 seconds for the third time and so on.
Important Notes: 15 and 5 lcm
The below are the important notes to be remembered while solving the lcm of 15 and 5:
- The common prime factors and the remaining prime factors of 15 and 5 should be multiplied to find the least common multiple of 15 and 5, when solving lcm by using prime factors method.
- The results of lcm of 15 and 5, and the lcm of 5 and 15 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 15 and 5?
The below solved example with step by step work shows how to find what is the lcm of 15 and 5 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 15 and 5?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 15
B = 5
What to be found:
find the lcm of 15 and 5
step 2 Find the prime factors of 15 and 5:
Prime factors of 15 = 3 x 5
Prime factors of 5 = 5
step 3 Identify the repeated and non-repeated prime factors of 15 and 5:
{5} is the most repeated factor and {3} is the non-repeated factor of 15 and 5.
step 4 Find the product of repeated and non-repeated prime factors of 15 and 5:
= 5 x 3
= 15
lcm(15 and 5) = 15
Hence,
lcm of 15 and 5 is 15
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 15 and 5.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 15 and 5
What to be found:
lcm (15, 5) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
15 and 5
step 3 Choose the divisor which divides each or most of the given integers (15 and 5), 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 15 and 5 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 3 | 15 | 5 |
| 5 | 5 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 15 and 5:
= 3 x 5
= 15
LCM(15, 5) = 15
The LCM of two numbers 15 and 5 is 15