LCM of 9, 12 and 16 is equal to 144. The comprehensive work provides more insight of how to find what is the lcm of 9, 12 and 16 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 16?
lcm (9 12 16) = (?)
9 => 3 x 3
12 => 2 x 2 x 3
16 => 2 x 2 x 2 x 2
= 2 x 2 x 3 x 3 x 2 x 2
= 144
lcm (9, 12 and 16) = 144
144 is the lcm of 9, 12 and 16.
where,
9 is a positive integer,
12 is a positive integer,
144 is the lcm of 9, 12 and 16,
{2, 2, 3} in {3 x 3, 2 x 2 x 3, 2 x 2 x 2 x 2} are the most repeated factors of 9, 12 and 16,
{3, 2, 2} in {3 x 3, 2 x 2 x 3, 2 x 2 x 2 x 2} are the the other remaining factors of 9, 12 and 16.
Use in Mathematics: LCM of 9, 12 and 16
The below are some of the mathematical applications where lcm of 9, 12 and 16 can be used:
- to find the least number which is exactly divisible by 9, 12 and 16.
- to find the common denominators for the fractions having 9, 12 and 16 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 9, 12 and 16 lcm
In the context of lcm real world problems, the lcm of 9, 12 and 16 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 16 seconds repeatedly. The answer is that all bells A, B and C toll together at 144 seconds for the first time, at 288 seconds for the second time, at 432 seconds for the third time and so on.
Important Notes: 9, 12 and 16 lcm
The below are the important notes to be remembered while solving the lcm of 9, 12 and 16:
- The repeated and non-repeated prime factors of 9, 12 and 16 should be multiplied to find the least common multiple of 9, 12 and 16, when solving lcm by using prime factors method.
- The results of lcm of 9, 12 and 16 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.