LCM of 6 and 332
996 is the LCM of 6 and 332. 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 6 and 332, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 6 and 332?
lcm (6 332) = (?)
6 => 2 x 3
332 => 2 x 2 x 83
= 2 x 3 x 2 x 83
= 996
lcm (6 and 332) = 996
996 is the LCM of 6 and 332.
where,
6 is a positive integer,
332 is a positive integer,
996 is the LCM of 6 and 332,
{2} in {2 x 3, 2 x 2 x 83} is the common factors of 6 and 332,
{3 x 2 x 83} in {2 x 3, 2 x 2 x 83} are the uncommon factors of 6 and 332.
Use in Mathematics: LCM of 6 and 332
The below are some of the mathematical applications where lcm of 6 and 332 can be used:
- to find the least number which is exactly divisible by 6 and 332.
- to find the common denominator for two fractions having 6 and 332 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 6 and 332 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 6 seconds and bell B tolls at 332 seconds repeatedly. The answer is that all bells A and B toll together at 996 seconds for the first time, at 1992 seconds for the second time, at 2988 seconds for the third time and so on.
Important Notes: 6 and 332 lcm
The below are the important notes to be remembered while solving the lcm of 6 and 332:
- The common prime factors and the remaining prime factors of 6 and 332 should be multiplied to find the least common multiple of 6 and 332, when solving lcm by using prime factors method.
- The results of lcm of 6 and 332, and the lcm of 332 and 6 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 6 and 332?
The below solved example with step by step work shows how to find what is the lcm of 6 and 332 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 6 and 332?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 6
B = 332
What to be found:
find the lcm of 6 and 332
step 2 Find the prime factors of 6 and 332:
Prime factors of 6 = 2 x 3
Prime factors of 332 = 2 x 2 x 83
step 3 Identify the repeated and non-repeated prime factors of 6 and 332:
{2} is the most repeated factor and {3 x 2 x 83} are the non-repeated factors of 6 and 332.
step 4 Find the product of repeated and non-repeated prime factors of 6 and 332:
= 2 x 3 x 2 x 83
= 996
lcm(6 and 332) = 996
Hence,
lcm of 6 and 332 is 996
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 6 and 332.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 6 and 332
What to be found:
lcm (6, 332) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
6 and 332
step 3 Choose the divisor which divides each or most of the given integers (6 and 332), 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 6 and 332 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 6 | 332 |
| 2 | 3 | 166 |
| 3 | 3 | 83 |
| 83 | 1 | 83 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 6 and 332:
= 2 x 2 x 3 x 83
= 996
LCM(6, 332) = 996
The LCM of two numbers 6 and 332 is 996