LCM of 24, 36 and 42 is equal to 504. The comprehensive work provides more insight of how to find what is the lcm of 24, 36 and 42 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 24, 36 and 42?
lcm (24 36 42) = (?)
24 => 2 x 2 x 2 x 3
36 => 2 x 2 x 3 x 3
42 => 2 x 3 x 7
= 2 x 2 x 3 x 2 x 3 x 7
= 504
lcm (24, 36 and 42) = 504
504 is the lcm of 24, 36 and 42.
where,
24 is a positive integer,
36 is a positive integer,
504 is the lcm of 24, 36 and 42,
{2, 2, 3} in {2 x 2 x 2 x 3, 2 x 2 x 3 x 3, 2 x 3 x 7} are the most repeated factors of 24, 36 and 42,
{2, 3, 7} in {2 x 2 x 2 x 3, 2 x 2 x 3 x 3, 2 x 3 x 7} are the the other remaining factors of 24, 36 and 42.
Use in Mathematics: LCM of 24, 36 and 42
The below are some of the mathematical applications where lcm of 24, 36 and 42 can be used:
- to find the least number which is exactly divisible by 24, 36 and 42.
- to find the common denominators for the fractions having 24, 36 and 42 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 24, 36 and 42 lcm
In the context of lcm real world problems, the lcm of 24, 36 and 42 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 24 seconds, B tolls at 36 seconds and C tolls at 42 seconds repeatedly. The answer is that all bells A, B and C toll together at 504 seconds for the first time, at 1008 seconds for the second time, at 1512 seconds for the third time and so on.
Important Notes: 24, 36 and 42 lcm
The below are the important notes to be remembered while solving the lcm of 24, 36 and 42:
- The repeated and non-repeated prime factors of 24, 36 and 42 should be multiplied to find the least common multiple of 24, 36 and 42, when solving lcm by using prime factors method.
- The results of lcm of 24, 36 and 42 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.