16, 30 and 35 LCM
LCM of 16, 30 and 35 is equal to 1680. The comprehensive work provides more insight of how to find what is the lcm of 16, 30 and 35 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 16, 30 and 35?
lcm (16 30 35) = (?)
16 => 2 x 2 x 2 x 2
30 => 2 x 3 x 5
35 => 5 x 7
= 2 x 5 x 2 x 2 x 2 x 3 x 7
= 1680
lcm (16, 30 and 35) = 1680
1680 is the lcm of 16, 30 and 35.
where,
16 is a positive integer,
30 is a positive integer,
1680 is the lcm of 16, 30 and 35,
{2, 5} in {2 x 2 x 2 x 2, 2 x 3 x 5, 5 x 7} are the most repeated factors of 16, 30 and 35,
{2, 2, 2, 3, 7} in {2 x 2 x 2 x 2, 2 x 3 x 5, 5 x 7} are the the other remaining factors of 16, 30 and 35.
Use in Mathematics: LCM of 16, 30 and 35
The below are some of the mathematical applications where lcm of 16, 30 and 35 can be used:
- to find the least number which is exactly divisible by 16, 30 and 35.
- to find the common denominators for the fractions having 16, 30 and 35 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 16, 30 and 35 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 16 seconds, B tolls at 30 seconds and C tolls at 35 seconds repeatedly. The answer is that all bells A, B and C toll together at 1680 seconds for the first time, at 3360 seconds for the second time, at 5040 seconds for the third time and so on.
Important Notes: 16, 30 and 35 lcm
The below are the important notes to be remembered while solving the lcm of 16, 30 and 35:
- The repeated and non-repeated prime factors of 16, 30 and 35 should be multiplied to find the least common multiple of 16, 30 and 35, when solving lcm by using prime factors method.
- The results of lcm of 16, 30 and 35 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 16, 30 and 35?
The below solved example with step by step work shows how to find what is the lcm of 16, 30 and 35 by using either prime factors method and special division method.
Solved example using prime factors method:
What is the LCM of 16, 30 and 35?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 16
B = 30
C = 35
What to be found:
find the lcm of 16, 30 and 35
step 2 Find the prime factors of 16, 30 and 35:
Prime factors of 16 = 2 x 2 x 2 x 2
Prime factors of 30 = 2 x 3 x 5
Prime factors of 35 = 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 16, 30 and 35:
{2, 5} are the most repeated factors and {2, 2, 2, 3, 7} are the non-repeated factors of 16, 30 and 35.
step 4 Find the product of repeated and non-repeated prime factors of 16, 30 and 35:
= 2 x 5 x 2 x 2 x 2 x 3 x 7
= 1680
lcm(20 and 30) = 1680
Hence,
lcm of 16, 30 and 35 is 1680
This special division method is the easiest way to understand the entire calculation of what is the lcm of 16, 30 and 35.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 16, 30 and 35
What to be found:
lcm (16, 30, 35) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
16, 30 and 35
step 3 Choose the divisor which divides each or most of the given integers (16, 30 and 35), 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 16, 30 and 35 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 16 | 30 | 35 |
| 2 | 8 | 15 | 35 |
| 2 | 4 | 15 | 35 |
| 2 | 2 | 15 | 35 |
| 3 | 1 | 15 | 35 |
| 5 | 1 | 5 | 35 |
| 7 | 1 | 1 | 7 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 16, 30 and 35:
= 2 x 2 x 2 x 2 x 3 x 5 x 7
= 1680
LCM(16, 30, 35) = 1680
The least common multiple for three numbers 16, 30 and 35 is 1680