LCM of 30 and 105 is equal to 210. The comprehensive work provides more insight of how to find what is the lcm of 30 and 105 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 30 and 105?
lcm (30 105) = (?)
30 => 2 x 3 x 5
105 => 3 x 5 x 7
= 3 x 5 x 2 x 7
= 210
lcm (30 and 105) = 210
210 is the lcm of 30 and 105.
where,
30 is a positive integer,
105 is a positive integer,
210 is the lcm of 30 and 105,
{3 x 5} in {2 x 3 x 5, 3 x 5 x 7} are the common factors of 30 and 105,
{2 x 7} in {2 x 3 x 5, 3 x 5 x 7} are the uncommon factors of 30 and 105.
Use in Mathematics: LCM of 30 and 105
The below are some of the mathematical applications where lcm of 30 and 105 can be used:
- to find the least number which is exactly divisible by 30 and 105.
- to find the common denominator for two fractions having 30 and 105 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 30 and 105 lcm
In the context of lcm real world problems, the lcm of 30 and 105 helps to find the exact time when two similar and recurring events 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 the bells A and B all toll together, if bell A tolls at 30 seconds and bell B tolls at 105 seconds repeatedly. The answer is that all bells A and B toll together at 210 seconds for the first time, at 420 seconds for the second time, at 630 seconds for the third time and so on.
Important Notes: 30 and 105 lcm
The below are the important notes to be remembered while solving the lcm of 30 and 105:
- The common prime factors and the remaining prime factors of 30 and 105 should be multiplied to find the least common multiple of 30 and 105, when solving lcm by using prime factors method.
- The results of lcm of 30 and 105, and the lcm of 105 and 30 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.