9, 12 and 14 LCM
LCM of 9, 12 and 14 is equal to 252. The comprehensive work provides more insight of how to find what is the lcm of 9, 12 and 14 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 9, 12 and 14?
lcm (9 12 14) = (?)
9 => 3 x 3
12 => 2 x 2 x 3
14 => 2 x 7
= 2 x 3 x 3 x 2 x 7
= 252
lcm (9, 12 and 14) = 252
252 is the lcm of 9, 12 and 14.
where,
9 is a positive integer,
12 is a positive integer,
252 is the lcm of 9, 12 and 14,
{2, 3} in {3 x 3, 2 x 2 x 3, 2 x 7} are the most repeated factors of 9, 12 and 14,
{3, 2, 7} in {3 x 3, 2 x 2 x 3, 2 x 7} are the the other remaining factors of 9, 12 and 14.
Use in Mathematics: LCM of 9, 12 and 14
The below are some of the mathematical applications where lcm of 9, 12 and 14 can be used:
- to find the least number which is exactly divisible by 9, 12 and 14.
- to find the common denominators for the fractions having 9, 12 and 14 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 9, 12 and 14 helps to find the exact time when three similar and recurring 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 all the bells A, B and C toll together, if bell A tolls at 9 seconds, B tolls at 12 seconds and C tolls at 14 seconds repeatedly. The answer is that all bells A, B and C toll together at 252 seconds for the first time, at 504 seconds for the second time, at 756 seconds for the third time and so on.
Important Notes: 9, 12 and 14 lcm
The below are the important notes to be remembered while solving the lcm of 9, 12 and 14:
- The repeated and non-repeated prime factors of 9, 12 and 14 should be multiplied to find the least common multiple of 9, 12 and 14, when solving lcm by using prime factors method.
- The results of lcm of 9, 12 and 14 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 9, 12 and 14?
The below solved example with step by step work shows how to find what is the lcm of 9, 12 and 14 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 9, 12 and 14?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 9
B = 12
C = 14
What to be found:
find the lcm of 9, 12 and 14
step 2 Find the prime factors of 9, 12 and 14:
Prime factors of 9 = 3 x 3
Prime factors of 12 = 2 x 2 x 3
Prime factors of 14 = 2 x 7
step 3 Identify the repeated and non-repeated prime factors of 9, 12 and 14:
{2, 3} are the most repeated factors and {3, 2, 7} are the non-repeated factors of 9, 12 and 14.
step 4 Find the product of repeated and non-repeated prime factors of 9, 12 and 14:
= 2 x 3 x 3 x 2 x 7
= 252
lcm(20 and 30) = 252
Hence,
lcm of 9, 12 and 14 is 252
This special division method is the easiest way to understand the entire calculation of what is the lcm of 9, 12 and 14.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 9, 12 and 14
What to be found:
lcm (9, 12, 14) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
9, 12 and 14
step 3 Choose the divisor which divides each or most of the given integers (9, 12 and 14), 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 9, 12 and 14 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 9 | 12 | 14 |
| 2 | 9 | 6 | 7 |
| 3 | 9 | 3 | 7 |
| 3 | 3 | 1 | 7 |
| 7 | 1 | 1 | 7 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 9, 12 and 14:
= 2 x 2 x 3 x 3 x 7
= 252
LCM(9, 12, 14) = 252
The least common multiple for three numbers 9, 12 and 14 is 252