LCM of 30 and 44
660 is the LCM of 30 and 44. 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 30 and 44, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 30 and 44?
lcm (30 44) = (?)
30 => 2 x 3 x 5
44 => 2 x 2 x 11
= 2 x 3 x 5 x 2 x 11
= 660
lcm (30 and 44) = 660
660 is the LCM of 30 and 44.
where,
30 is a positive integer,
44 is a positive integer,
660 is the LCM of 30 and 44,
{2} in {2 x 3 x 5, 2 x 2 x 11} is the common factors of 30 and 44,
{3 x 5 x 2 x 11} in {2 x 3 x 5, 2 x 2 x 11} are the uncommon factors of 30 and 44.
Use in Mathematics: LCM of 30 and 44
The below are some of the mathematical applications where lcm of 30 and 44 can be used:
- to find the least number which is exactly divisible by 30 and 44.
- to find the common denominator for two fractions having 30 and 44 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 30 and 44 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 30 seconds and bell B tolls at 44 seconds repeatedly. The answer is that all bells A and B toll together at 660 seconds for the first time, at 1320 seconds for the second time, at 1980 seconds for the third time and so on.
Important Notes: 30 and 44 lcm
The below are the important notes to be remembered while solving the lcm of 30 and 44:
- The common prime factors and the remaining prime factors of 30 and 44 should be multiplied to find the least common multiple of 30 and 44, when solving lcm by using prime factors method.
- The results of lcm of 30 and 44, and the lcm of 44 and 30 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 30 and 44?
The below solved example with step by step work shows how to find what is the lcm of 30 and 44 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 30 and 44?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 30
B = 44
What to be found:
find the lcm of 30 and 44
step 2 Find the prime factors of 30 and 44:
Prime factors of 30 = 2 x 3 x 5
Prime factors of 44 = 2 x 2 x 11
step 3 Identify the repeated and non-repeated prime factors of 30 and 44:
{2} is the most repeated factor and {3 x 5 x 2 x 11} are the non-repeated factors of 30 and 44.
step 4 Find the product of repeated and non-repeated prime factors of 30 and 44:
= 2 x 3 x 5 x 2 x 11
= 660
lcm(30 and 44) = 660
Hence,
lcm of 30 and 44 is 660
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 30 and 44.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 30 and 44
What to be found:
lcm (30, 44) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
30 and 44
step 3 Choose the divisor which divides each or most of the given integers (30 and 44), 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 30 and 44 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 30 | 44 |
| 2 | 15 | 22 |
| 3 | 15 | 11 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 30 and 44:
= 2 x 2 x 3 x 5 x 11
= 660
LCM(30, 44) = 660
The LCM of two numbers 30 and 44 is 660