70, 75 and 80 LCM
LCM of 70, 75 and 80 is equal to 8400. The comprehensive work provides more insight of how to find what is the lcm of 70, 75 and 80 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 70, 75 and 80?
lcm (70 75 80) = (?)
70 => 2 x 5 x 7
75 => 3 x 5 x 5
80 => 2 x 2 x 2 x 2 x 5
= 2 x 5 x 7 x 3 x 5 x 2 x 2 x 2
= 8400
lcm (70, 75 and 80) = 8400
8400 is the lcm of 70, 75 and 80.
where,
70 is a positive integer,
75 is a positive integer,
8400 is the lcm of 70, 75 and 80,
{2, 5} in {2 x 5 x 7, 3 x 5 x 5, 2 x 2 x 2 x 2 x 5} are the most repeated factors of 70, 75 and 80,
{7, 3, 5, 2, 2, 2} in {2 x 5 x 7, 3 x 5 x 5, 2 x 2 x 2 x 2 x 5} are the the other remaining factors of 70, 75 and 80.
Use in Mathematics: LCM of 70, 75 and 80
The below are some of the mathematical applications where lcm of 70, 75 and 80 can be used:
- to find the least number which is exactly divisible by 70, 75 and 80.
- to find the common denominators for the fractions having 70, 75 and 80 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 70, 75 and 80 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 70 seconds, B tolls at 75 seconds and C tolls at 80 seconds repeatedly. The answer is that all bells A, B and C toll together at 8400 seconds for the first time, at 16800 seconds for the second time, at 25200 seconds for the third time and so on.
Important Notes: 70, 75 and 80 lcm
The below are the important notes to be remembered while solving the lcm of 70, 75 and 80:
- The repeated and non-repeated prime factors of 70, 75 and 80 should be multiplied to find the least common multiple of 70, 75 and 80, when solving lcm by using prime factors method.
- The results of lcm of 70, 75 and 80 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 70, 75 and 80?
The below solved example with step by step work shows how to find what is the lcm of 70, 75 and 80 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 70, 75 and 80?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 70
B = 75
C = 80
What to be found:
find the lcm of 70, 75 and 80
step 2 Find the prime factors of 70, 75 and 80:
Prime factors of 70 = 2 x 5 x 7
Prime factors of 75 = 3 x 5 x 5
Prime factors of 80 = 2 x 2 x 2 x 2 x 5
step 3 Identify the repeated and non-repeated prime factors of 70, 75 and 80:
{2, 5} are the most repeated factors and {7, 3, 5, 2, 2, 2} are the non-repeated factors of 70, 75 and 80.
step 4 Find the product of repeated and non-repeated prime factors of 70, 75 and 80:
= 2 x 5 x 7 x 3 x 5 x 2 x 2 x 2
= 8400
lcm(20 and 30) = 8400
Hence,
lcm of 70, 75 and 80 is 8400
This special division method is the easiest way to understand the entire calculation of what is the lcm of 70, 75 and 80.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 70, 75 and 80
What to be found:
lcm (70, 75, 80) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
70, 75 and 80
step 3 Choose the divisor which divides each or most of the given integers (70, 75 and 80), 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 70, 75 and 80 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 70 | 75 | 80 |
| 2 | 35 | 75 | 40 |
| 2 | 35 | 75 | 20 |
| 2 | 35 | 75 | 10 |
| 3 | 35 | 75 | 5 |
| 5 | 35 | 25 | 5 |
| 5 | 7 | 5 | 1 |
| 7 | 7 | 1 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 70, 75 and 80:
= 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7
= 8400
LCM(70, 75, 80) = 8400
The least common multiple for three numbers 70, 75 and 80 is 8400