LCM of 12, 24 and 72 is equal to 72. The comprehensive work provides more insight of how to find what is the lcm of 12, 24 and 72 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 12, 24 and 72?
lcm (12 24 72) = (?)
12 => 2 x 2 x 3
24 => 2 x 2 x 2 x 3
72 => 2 x 2 x 2 x 3 x 3
= 2 x 2 x 2 x 3 x 3
= 72
lcm (12, 24 and 72) = 72
72 is the lcm of 12, 24 and 72.
where,
12 is a positive integer,
24 is a positive integer,
72 is the lcm of 12, 24 and 72,
{2, 2, 2, 3} in {2 x 2 x 3, 2 x 2 x 2 x 3, 2 x 2 x 2 x 3 x 3} are the most repeated factors of 12, 24 and 72,
{3} in {2 x 2 x 3, 2 x 2 x 2 x 3, 2 x 2 x 2 x 3 x 3} is the other remaining factors of 12, 24 and 72.
Use in Mathematics: LCM of 12, 24 and 72
The below are some of the mathematical applications where lcm of 12, 24 and 72 can be used:
- to find the least number which is exactly divisible by 12, 24 and 72.
- to find the common denominators for the fractions having 12, 24 and 72 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 12, 24 and 72 lcm
In the context of lcm real world problems, the lcm of 12, 24 and 72 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 12 seconds, B tolls at 24 seconds and C tolls at 72 seconds repeatedly. The answer is that all bells A, B and C toll together at 72 seconds for the first time, at 144 seconds for the second time, at 216 seconds for the third time and so on.
Important Notes: 12, 24 and 72 lcm
The below are the important notes to be remembered while solving the lcm of 12, 24 and 72:
- The repeated and non-repeated prime factors of 12, 24 and 72 should be multiplied to find the least common multiple of 12, 24 and 72, when solving lcm by using prime factors method.
- The results of lcm of 12, 24 and 72 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.