LCM of 64 and 68
1088 is the LCM of 64 and 68. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 64 and 68, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 64 and 68?
lcm (64 68) = (?)
64 => 2 x 2 x 2 x 2 x 2 x 2
68 => 2 x 2 x 17
= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
lcm (64 and 68) = 1088
1088 is the LCM of 64 and 68.
where,
64 is a positive integer,
68 is a positive integer,
1088 is the LCM of 64 and 68,
{2 x 2} in {2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 17} are the common factors of 64 and 68,
{2 x 2 x 2 x 2 x 17} in {2 x 2 x 2 x 2 x 2 x 2, 2 x 2 x 17} are the uncommon factors of 64 and 68.
Use in Mathematics: LCM of 64 and 68
The below are some of the mathematical applications where lcm of 64 and 68 can be used:
- to find the least number which is exactly divisible by 64 and 68.
- to find the common denominator for two fractions having 64 and 68 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 64 and 68 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 64 seconds and bell B tolls at 68 seconds repeatedly. The answer is that all bells A and B toll together at 1088 seconds for the first time, at 2176 seconds for the second time, at 3264 seconds for the third time and so on.
Important Notes: 64 and 68 lcm
The below are the important notes to be remembered while solving the lcm of 64 and 68:
- The common prime factors and the remaining prime factors of 64 and 68 should be multiplied to find the least common multiple of 64 and 68, when solving lcm by using prime factors method.
- The results of lcm of 64 and 68, and the lcm of 68 and 64 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 64 and 68?
The below solved example with step by step work shows how to find what is the lcm of 64 and 68 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 64 and 68?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 64
B = 68
What to be found:
find the lcm of 64 and 68
step 2 Find the prime factors of 64 and 68:
Prime factors of 64 = 2 x 2 x 2 x 2 x 2 x 2
Prime factors of 68 = 2 x 2 x 17
step 3 Identify the repeated and non-repeated prime factors of 64 and 68:
{2, 2} are the most repeated factors and {2 x 2 x 2 x 2 x 17} are the non-repeated factors of 64 and 68.
step 4 Find the product of repeated and non-repeated prime factors of 64 and 68:
= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
lcm(64 and 68) = 1088
Hence,
lcm of 64 and 68 is 1088
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 64 and 68.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 64 and 68
What to be found:
lcm (64, 68) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
64 and 68
step 3 Choose the divisor which divides each or most of the given integers (64 and 68), 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 64 and 68 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 64 | 68 |
| 2 | 32 | 34 |
| 2 | 16 | 17 |
| 2 | 8 | 17 |
| 2 | 4 | 17 |
| 2 | 2 | 17 |
| 17 | 1 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 64 and 68:
= 2 x 2 x 2 x 2 x 2 x 2 x 17
= 1088
LCM(64, 68) = 1088
The LCM of two numbers 64 and 68 is 1088