36 and 140 LCM
LCM of 36 and 140 is equal to 1260. The comprehensive work provides more insight of how to find what is the lcm of 36 and 140 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 36 and 140?
lcm (36 140) = (?)
36 => 2 x 2 x 3 x 3
140 => 2 x 2 x 5 x 7
= 2 x 2 x 3 x 3 x 5 x 7
= 1260
lcm (36 and 140) = 1260
1260 is the lcm of 36 and 140.
where,
36 is a positive integer,
140 is a positive integer,
1260 is the lcm of 36 and 140,
{2 x 2} in {2 x 2 x 3 x 3, 2 x 2 x 5 x 7} are the common factors of 36 and 140,
{3 x 3 x 5 x 7} in {2 x 2 x 3 x 3, 2 x 2 x 5 x 7} are the uncommon factors of 36 and 140.
Use in Mathematics: LCM of 36 and 140
The below are some of the mathematical applications where lcm of 36 and 140 can be used:
- to find the least number which is exactly divisible by 36 and 140.
- to find the common denominator for two fractions having 36 and 140 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 36 and 140 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 36 seconds and bell B tolls at 140 seconds repeatedly. The answer is that all bells A and B toll together at 1260 seconds for the first time, at 2520 seconds for the second time, at 3780 seconds for the third time and so on.
Important Notes: 36 and 140 lcm
The below are the important notes to be remembered while solving the lcm of 36 and 140:
- The common prime factors and the remaining prime factors of 36 and 140 should be multiplied to find the least common multiple of 36 and 140, when solving lcm by using prime factors method.
- The results of lcm of 36 and 140, and the lcm of 140 and 36 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 36 and 140?
The below solved example with step by step work shows how to find what is the lcm of 36 and 140 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 36 and 140?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 36
B = 140
What to be found:
find the lcm of 36 and 140
step 2 Find the prime factors of 36 and 140:
Prime factors of 36 = 2 x 2 x 3 x 3
Prime factors of 140 = 2 x 2 x 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 36 and 140:
{2, 2} are the most repeated factors and {3 x 3 x 5 x 7} are the non-repeated factors of 36 and 140.
step 4 Find the product of repeated and non-repeated prime factors of 36 and 140:
= 2 x 2 x 3 x 3 x 5 x 7
= 1260
lcm(36 and 140) = 1260
Hence,
lcm of 36 and 140 is 1260
This special division method is the easiest way to understand the entire calculation of what is the lcm of 36 and 140.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 36 and 140
What to be found:
lcm (36, 140) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
36 and 140
step 3 Choose the divisor which divides each or most of the given integers (36 and 140), 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 36 and 140 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 36 | 140 |
| 2 | 18 | 70 |
| 3 | 9 | 35 |
| 3 | 3 | 35 |
| 5 | 1 | 35 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 36 and 140:
= 2 x 2 x 3 x 3 x 5 x 7
= 1260
LCM(36, 140) = 1260
The least common multiple for two numbers 36 and 140 is 1260