LCM of 8, 12 and 15 is equal to 120. The comprehensive work provides more insight of how to find what is the lcm of 8, 12 and 15 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 8, 12 and 15?
lcm (8 12 15) = (?)
8 => 2 x 2 x 2
12 => 2 x 2 x 3
15 => 3 x 5
= 2 x 2 x 3 x 2 x 5
= 120
lcm (8, 12 and 15) = 120
120 is the lcm of 8, 12 and 15.
where,
8 is a positive integer,
12 is a positive integer,
120 is the lcm of 8, 12 and 15,
{2, 2, 3} in {2 x 2 x 2, 2 x 2 x 3, 3 x 5} are the most repeated factors of 8, 12 and 15,
{2, 5} in {2 x 2 x 2, 2 x 2 x 3, 3 x 5} are the the other remaining factors of 8, 12 and 15.
Use in Mathematics: LCM of 8, 12 and 15
The below are some of the mathematical applications where lcm of 8, 12 and 15 can be used:
- to find the least number which is exactly divisible by 8, 12 and 15.
- to find the common denominators for the fractions having 8, 12 and 15 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 8, 12 and 15 lcm
In the context of lcm real world problems, the lcm of 8, 12 and 15 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 8 seconds, B tolls at 12 seconds and C tolls at 15 seconds repeatedly. The answer is that all bells A, B and C toll together at 120 seconds for the first time, at 240 seconds for the second time, at 360 seconds for the third time and so on.
Important Notes: 8, 12 and 15 lcm
The below are the important notes to be remembered while solving the lcm of 8, 12 and 15:
- The repeated and non-repeated prime factors of 8, 12 and 15 should be multiplied to find the least common multiple of 8, 12 and 15, when solving lcm by using prime factors method.
- The results of lcm of 8, 12 and 15 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.