LCM of 138 and 210
4830 is the LCM of 138 and 210. 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 138 and 210, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 138 and 210?
lcm (138 210) = (?)
138 => 2 x 3 x 23
210 => 2 x 3 x 5 x 7
= 2 x 3 x 23 x 5 x 7
= 4830
lcm (138 and 210) = 4830
4830 is the LCM of 138 and 210.
where,
138 is a positive integer,
210 is a positive integer,
4830 is the LCM of 138 and 210,
{2 x 3} in {2 x 3 x 23, 2 x 3 x 5 x 7} are the common factors of 138 and 210,
{23 x 5 x 7} in {2 x 3 x 23, 2 x 3 x 5 x 7} are the uncommon factors of 138 and 210.
Use in Mathematics: LCM of 138 and 210
The below are some of the mathematical applications where lcm of 138 and 210 can be used:
- to find the least number which is exactly divisible by 138 and 210.
- to find the common denominator for two fractions having 138 and 210 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 138 and 210 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 138 seconds and bell B tolls at 210 seconds repeatedly. The answer is that all bells A and B toll together at 4830 seconds for the first time, at 9660 seconds for the second time, at 14490 seconds for the third time and so on.
Important Notes: 138 and 210 lcm
The below are the important notes to be remembered while solving the lcm of 138 and 210:
- The common prime factors and the remaining prime factors of 138 and 210 should be multiplied to find the least common multiple of 138 and 210, when solving lcm by using prime factors method.
- The results of lcm of 138 and 210, and the lcm of 210 and 138 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 138 and 210?
The below solved example with step by step work shows how to find what is the lcm of 138 and 210 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 138 and 210?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 138
B = 210
What to be found:
find the lcm of 138 and 210
step 2 Find the prime factors of 138 and 210:
Prime factors of 138 = 2 x 3 x 23
Prime factors of 210 = 2 x 3 x 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 138 and 210:
{2, 3} are the most repeated factors and {23 x 5 x 7} are the non-repeated factors of 138 and 210.
step 4 Find the product of repeated and non-repeated prime factors of 138 and 210:
= 2 x 3 x 23 x 5 x 7
= 4830
lcm(138 and 210) = 4830
Hence,
lcm of 138 and 210 is 4830
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 138 and 210.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 138 and 210
What to be found:
lcm (138, 210) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
138 and 210
step 3 Choose the divisor which divides each or most of the given integers (138 and 210), 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 138 and 210 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 138 | 210 |
| 3 | 69 | 105 |
| 5 | 23 | 35 |
| 7 | 23 | 7 |
| 23 | 23 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 138 and 210:
= 2 x 3 x 5 x 7 x 23
= 4830
LCM(138, 210) = 4830
The LCM of two numbers 138 and 210 is 4830