LCM of 57 and 6
114 is the LCM of 57 and 6. 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 57 and 6, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 57 and 6?
lcm (57 6) = (?)
57 => 3 x 19
6 => 2 x 3
= 3 x 19 x 2
= 114
lcm (57 and 6) = 114
114 is the LCM of 57 and 6.
where,
57 is a positive integer,
6 is a positive integer,
114 is the LCM of 57 and 6,
{3} in {3 x 19, 2 x 3} is the common factors of 57 and 6,
{19 x 2} in {3 x 19, 2 x 3} are the uncommon factors of 57 and 6.
Use in Mathematics: LCM of 57 and 6
The below are some of the mathematical applications where lcm of 57 and 6 can be used:
- to find the least number which is exactly divisible by 57 and 6.
- to find the common denominator for two fractions having 57 and 6 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 57 and 6 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 57 seconds and bell B tolls at 6 seconds repeatedly. The answer is that all bells A and B toll together at 114 seconds for the first time, at 228 seconds for the second time, at 342 seconds for the third time and so on.
Important Notes: 57 and 6 lcm
The below are the important notes to be remembered while solving the lcm of 57 and 6:
- The common prime factors and the remaining prime factors of 57 and 6 should be multiplied to find the least common multiple of 57 and 6, when solving lcm by using prime factors method.
- The results of lcm of 57 and 6, and the lcm of 6 and 57 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 57 and 6?
The below solved example with step by step work shows how to find what is the lcm of 57 and 6 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 57 and 6?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 57
B = 6
What to be found:
find the lcm of 57 and 6
step 2 Find the prime factors of 57 and 6:
Prime factors of 57 = 3 x 19
Prime factors of 6 = 2 x 3
step 3 Identify the repeated and non-repeated prime factors of 57 and 6:
{3} is the most repeated factor and {19 x 2} are the non-repeated factors of 57 and 6.
step 4 Find the product of repeated and non-repeated prime factors of 57 and 6:
= 3 x 19 x 2
= 114
lcm(57 and 6) = 114
Hence,
lcm of 57 and 6 is 114
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 57 and 6.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 57 and 6
What to be found:
lcm (57, 6) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
57 and 6
step 3 Choose the divisor which divides each or most of the given integers (57 and 6), 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 57 and 6 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 57 | 6 |
| 3 | 57 | 3 |
| 19 | 19 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 57 and 6:
= 2 x 3 x 19
= 114
LCM(57, 6) = 114
The LCM of two numbers 57 and 6 is 114