12, 14 and 42 LCM
LCM of 12, 14 and 42 is equal to 84. The comprehensive work provides more insight of how to find what is the lcm of 12, 14 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 12, 14 and 42?
lcm (12 14 42) = (?)
12 => 2 x 2 x 3
14 => 2 x 7
42 => 2 x 3 x 7
= 2 x 3 x 7 x 2
= 84
lcm (12, 14 and 42) = 84
84 is the lcm of 12, 14 and 42.
where,
12 is a positive integer,
14 is a positive integer,
84 is the lcm of 12, 14 and 42,
{2, 3, 7} in {2 x 2 x 3, 2 x 7, 2 x 3 x 7} are the most repeated factors of 12, 14 and 42,
{2} in {2 x 2 x 3, 2 x 7, 2 x 3 x 7} is the other remaining factors of 12, 14 and 42.
Use in Mathematics: LCM of 12, 14 and 42
The below are some of the mathematical applications where lcm of 12, 14 and 42 can be used:
- to find the least number which is exactly divisible by 12, 14 and 42.
- to find the common denominators for the fractions having 12, 14 and 42 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12, 14 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 12 seconds, B tolls at 14 seconds and C tolls at 42 seconds repeatedly. The answer is that all bells A, B and C toll together at 84 seconds for the first time, at 168 seconds for the second time, at 252 seconds for the third time and so on.
Important Notes: 12, 14 and 42 lcm
The below are the important notes to be remembered while solving the lcm of 12, 14 and 42:
- The repeated and non-repeated prime factors of 12, 14 and 42 should be multiplied to find the least common multiple of 12, 14 and 42, when solving lcm by using prime factors method.
- The results of lcm of 12, 14 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.
How-to: What is the LCM of 12, 14 and 42?
The below solved example with step by step work shows how to find what is the lcm of 12, 14 and 42 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 12, 14 and 42?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 14
C = 42
What to be found:
find the lcm of 12, 14 and 42
step 2 Find the prime factors of 12, 14 and 42:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 14 = 2 x 7
Prime factors of 42 = 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 12, 14 and 42:
{2, 3, 7} are the most repeated factors and {2} is the non-repeated factors of 12, 14 and 42.
step 4 Find the product of repeated and non-repeated prime factors of 12, 14 and 42:
= 2 x 3 x 7 x 2
= 84
lcm(20 and 30) = 84
Hence,
lcm of 12, 14 and 42 is 84
This special division method is the easiest way to understand the entire calculation of what is the lcm of 12, 14 and 42.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12, 14 and 42
What to be found:
lcm (12, 14, 42) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12, 14 and 42
step 3 Choose the divisor which divides each or most of the given integers (12, 14 and 42), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 12, 14 and 42 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 14 | 42 |
| 2 | 6 | 7 | 21 |
| 3 | 3 | 7 | 21 |
| 7 | 1 | 7 | 7 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12, 14 and 42:
= 2 x 2 x 3 x 7
= 84
LCM(12, 14, 42) = 84
The least common multiple for three numbers 12, 14 and 42 is 84