42, 70 and 84 LCM
LCM of 42, 70 and 84 is equal to 420. The comprehensive work provides more insight of how to find what is the lcm of 42, 70 and 84 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 42, 70 and 84?
lcm (42 70 84) = (?)
42 => 2 x 3 x 7
70 => 2 x 5 x 7
84 => 2 x 2 x 3 x 7
= 2 x 3 x 7 x 5 x 2
= 420
lcm (42, 70 and 84) = 420
420 is the lcm of 42, 70 and 84.
where,
42 is a positive integer,
70 is a positive integer,
420 is the lcm of 42, 70 and 84,
{2, 3, 7} in {2 x 3 x 7, 2 x 5 x 7, 2 x 2 x 3 x 7} are the most repeated factors of 42, 70 and 84,
{5, 2} in {2 x 3 x 7, 2 x 5 x 7, 2 x 2 x 3 x 7} are the the other remaining factors of 42, 70 and 84.
Use in Mathematics: LCM of 42, 70 and 84
The below are some of the mathematical applications where lcm of 42, 70 and 84 can be used:
- to find the least number which is exactly divisible by 42, 70 and 84.
- to find the common denominators for the fractions having 42, 70 and 84 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 42, 70 and 84 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 42 seconds, B tolls at 70 seconds and C tolls at 84 seconds repeatedly. The answer is that all bells A, B and C toll together at 420 seconds for the first time, at 840 seconds for the second time, at 1260 seconds for the third time and so on.
Important Notes: 42, 70 and 84 lcm
The below are the important notes to be remembered while solving the lcm of 42, 70 and 84:
- The repeated and non-repeated prime factors of 42, 70 and 84 should be multiplied to find the least common multiple of 42, 70 and 84, when solving lcm by using prime factors method.
- The results of lcm of 42, 70 and 84 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 42, 70 and 84?
The below solved example with step by step work shows how to find what is the lcm of 42, 70 and 84 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 42, 70 and 84?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 42
B = 70
C = 84
What to be found:
find the lcm of 42, 70 and 84
step 2 Find the prime factors of 42, 70 and 84:
Prime factors of 42 = 2 x 3 x 7
Prime factors of 70 = 2 x 5 x 7
Prime factors of 84 = 2 x 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 42, 70 and 84:
{2, 3, 7} are the most repeated factors and {5, 2} are the non-repeated factors of 42, 70 and 84.
step 4 Find the product of repeated and non-repeated prime factors of 42, 70 and 84:
= 2 x 3 x 7 x 5 x 2
= 420
lcm(20 and 30) = 420
Hence,
lcm of 42, 70 and 84 is 420
This special division method is the easiest way to understand the entire calculation of what is the lcm of 42, 70 and 84.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 42, 70 and 84
What to be found:
lcm (42, 70, 84) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
42, 70 and 84
step 3 Choose the divisor which divides each or most of the given integers (42, 70 and 84), 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 42, 70 and 84 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 42 | 70 | 84 |
| 2 | 21 | 35 | 42 |
| 3 | 21 | 35 | 21 |
| 5 | 7 | 35 | 7 |
| 7 | 7 | 7 | 7 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 42, 70 and 84:
= 2 x 2 x 3 x 5 x 7
= 420
LCM(42, 70, 84) = 420
The least common multiple for three numbers 42, 70 and 84 is 420