LCM of 233 and 332
77356 is the LCM of 233 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 233 and 332, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 233 and 332?
lcm (233 332) = (?)
233 => 233
332 => 2 x 2 x 83
= 233 x 2 x 2 x 83
= 77356
lcm (233 and 332) = 77356
77356 is the LCM of 233 and 332.
where,
233 is a positive integer,
332 is a positive integer,
77356 is the LCM of 233 and 332,
There is no common factors of 233 and 332 in {233, 2 x 2 x 83},
{233 x 2 x 2 x 83} in {233, 2 x 2 x 83} are the uncommon factors of 233 and 332.
Use in Mathematics: LCM of 233 and 332
The below are some of the mathematical applications where lcm of 233 and 332 can be used:
- to find the least number which is exactly divisible by 233 and 332.
- to find the common denominator for two fractions having 233 and 332 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 233 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 233 seconds and bell B tolls at 332 seconds repeatedly. The answer is that all bells A and B toll together at 77356 seconds for the first time, at 154712 seconds for the second time, at 232068 seconds for the third time and so on.
Important Notes: 233 and 332 lcm
The below are the important notes to be remembered while solving the lcm of 233 and 332:
- The common prime factors and the remaining prime factors of 233 and 332 should be multiplied to find the least common multiple of 233 and 332, when solving lcm by using prime factors method.
- The results of lcm of 233 and 332, and the lcm of 332 and 233 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 233 and 332?
The below solved example with step by step work shows how to find what is the lcm of 233 and 332 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 233 and 332?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 233
B = 332
What to be found:
find the lcm of 233 and 332
step 2 Find the prime factors of 233 and 332:
Prime factors of 233 = 233
Prime factors of 332 = 2 x 2 x 83
step 3Identify the repeated and non-repeated prime factors of 233 and 332:
Since there is no common factors between 233 and 332, multiplying the given numbers directly provides the LCM of
233 and 332.
= 233 x 332
= 77356
lcm(233 and 332) = 77356
Hence,
lcm of 233 and 332 is 77356
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 233 and 332.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 233 and 332
What to be found:
lcm (233, 332) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
233 and 332
step 3 Choose the divisor which divides each or most of the given integers (233 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 233 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 | 233 | 332 |
| 2 | 233 | 166 |
| 83 | 233 | 83 |
| 233 | 233 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 233 and 332:
= 2 x 2 x 83 x 233
= 77356
LCM(233, 332) = 77356
The LCM of two numbers 233 and 332 is 77356