LCM of 212 and 302
32012 is the LCM of 212 and 302. 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 212 and 302, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 212 and 302?
lcm (212 302) = (?)
212 => 2 x 2 x 53
302 => 2 x 151
= 2 x 2 x 53 x 151
= 32012
lcm (212 and 302) = 32012
32012 is the LCM of 212 and 302.
where,
212 is a positive integer,
302 is a positive integer,
32012 is the LCM of 212 and 302,
{2} in {2 x 2 x 53, 2 x 151} is the common factors of 212 and 302,
{2 x 53 x 151} in {2 x 2 x 53, 2 x 151} are the uncommon factors of 212 and 302.
Use in Mathematics: LCM of 212 and 302
The below are some of the mathematical applications where lcm of 212 and 302 can be used:
- to find the least number which is exactly divisible by 212 and 302.
- to find the common denominator for two fractions having 212 and 302 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 212 and 302 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 212 seconds and bell B tolls at 302 seconds repeatedly. The answer is that all bells A and B toll together at 32012 seconds for the first time, at 64024 seconds for the second time, at 96036 seconds for the third time and so on.
Important Notes: 212 and 302 lcm
The below are the important notes to be remembered while solving the lcm of 212 and 302:
- The common prime factors and the remaining prime factors of 212 and 302 should be multiplied to find the least common multiple of 212 and 302, when solving lcm by using prime factors method.
- The results of lcm of 212 and 302, and the lcm of 302 and 212 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 212 and 302?
The below solved example with step by step work shows how to find what is the lcm of 212 and 302 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 212 and 302?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 212
B = 302
What to be found:
find the lcm of 212 and 302
step 2 Find the prime factors of 212 and 302:
Prime factors of 212 = 2 x 2 x 53
Prime factors of 302 = 2 x 151
step 3 Identify the repeated and non-repeated prime factors of 212 and 302:
{2} is the most repeated factor and {2 x 53 x 151} are the non-repeated factors of 212 and 302.
step 4 Find the product of repeated and non-repeated prime factors of 212 and 302:
= 2 x 2 x 53 x 151
= 32012
lcm(212 and 302) = 32012
Hence,
lcm of 212 and 302 is 32012
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 212 and 302.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 212 and 302
What to be found:
lcm (212, 302) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
212 and 302
step 3 Choose the divisor which divides each or most of the given integers (212 and 302), 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 212 and 302 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 212 | 302 |
| 2 | 106 | 151 |
| 53 | 53 | 151 |
| 151 | 1 | 151 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 212 and 302:
= 2 x 2 x 53 x 151
= 32012
LCM(212, 302) = 32012
The LCM of two numbers 212 and 302 is 32012