LCM of 210 and 348
12180 is the LCM of 210 and 348. 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 210 and 348, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 210 and 348?
lcm (210 348) = (?)
210 => 2 x 3 x 5 x 7
348 => 2 x 2 x 3 x 29
= 2 x 3 x 5 x 7 x 2 x 29
= 12180
lcm (210 and 348) = 12180
12180 is the LCM of 210 and 348.
where,
210 is a positive integer,
348 is a positive integer,
12180 is the LCM of 210 and 348,
{2 x 3} in {2 x 3 x 5 x 7, 2 x 2 x 3 x 29} are the common factors of 210 and 348,
{5 x 7 x 2 x 29} in {2 x 3 x 5 x 7, 2 x 2 x 3 x 29} are the uncommon factors of 210 and 348.
Use in Mathematics: LCM of 210 and 348
The below are some of the mathematical applications where lcm of 210 and 348 can be used:
- to find the least number which is exactly divisible by 210 and 348.
- to find the common denominator for two fractions having 210 and 348 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 210 and 348 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 210 seconds and bell B tolls at 348 seconds repeatedly. The answer is that all bells A and B toll together at 12180 seconds for the first time, at 24360 seconds for the second time, at 36540 seconds for the third time and so on.
Important Notes: 210 and 348 lcm
The below are the important notes to be remembered while solving the lcm of 210 and 348:
- The common prime factors and the remaining prime factors of 210 and 348 should be multiplied to find the least common multiple of 210 and 348, when solving lcm by using prime factors method.
- The results of lcm of 210 and 348, and the lcm of 348 and 210 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 210 and 348?
The below solved example with step by step work shows how to find what is the lcm of 210 and 348 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 210 and 348?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 210
B = 348
What to be found:
find the lcm of 210 and 348
step 2 Find the prime factors of 210 and 348:
Prime factors of 210 = 2 x 3 x 5 x 7
Prime factors of 348 = 2 x 2 x 3 x 29
step 3 Identify the repeated and non-repeated prime factors of 210 and 348:
{2, 3} are the most repeated factors and {5 x 7 x 2 x 29} are the non-repeated factors of 210 and 348.
step 4 Find the product of repeated and non-repeated prime factors of 210 and 348:
= 2 x 3 x 5 x 7 x 2 x 29
= 12180
lcm(210 and 348) = 12180
Hence,
lcm of 210 and 348 is 12180
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 210 and 348.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 210 and 348
What to be found:
lcm (210, 348) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
210 and 348
step 3 Choose the divisor which divides each or most of the given integers (210 and 348), 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 210 and 348 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 210 | 348 |
| 2 | 105 | 174 |
| 3 | 105 | 87 |
| 5 | 35 | 29 |
| 7 | 7 | 29 |
| 29 | 1 | 29 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 210 and 348:
= 2 x 2 x 3 x 5 x 7 x 29
= 12180
LCM(210, 348) = 12180
The LCM of two numbers 210 and 348 is 12180