LCM of 45 and 64
2880 is the LCM of 45 and 64. 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 45 and 64, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 45 and 64?
lcm (45 64) = (?)
45 => 3 x 3 x 5
64 => 2 x 2 x 2 x 2 x 2 x 2
= 3 x 3 x 5 x 2 x 2 x 2 x 2 x 2 x 2
= 2880
lcm (45 and 64) = 2880
2880 is the LCM of 45 and 64.
where,
45 is a positive integer,
64 is a positive integer,
2880 is the LCM of 45 and 64,
There is no common factors of 45 and 64 in {3 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2},
{3 x 3 x 5 x 2 x 2 x 2 x 2 x 2 x 2} in {3 x 3 x 5, 2 x 2 x 2 x 2 x 2 x 2} are the uncommon factors of 45 and 64.
Use in Mathematics: LCM of 45 and 64
The below are some of the mathematical applications where lcm of 45 and 64 can be used:
- to find the least number which is exactly divisible by 45 and 64.
- to find the common denominator for two fractions having 45 and 64 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 45 and 64 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 45 seconds and bell B tolls at 64 seconds repeatedly. The answer is that all bells A and B toll together at 2880 seconds for the first time, at 5760 seconds for the second time, at 8640 seconds for the third time and so on.
Important Notes: 45 and 64 lcm
The below are the important notes to be remembered while solving the lcm of 45 and 64:
- The common prime factors and the remaining prime factors of 45 and 64 should be multiplied to find the least common multiple of 45 and 64, when solving lcm by using prime factors method.
- The results of lcm of 45 and 64, and the lcm of 64 and 45 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 45 and 64?
The below solved example with step by step work shows how to find what is the lcm of 45 and 64 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 45 and 64?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 45
B = 64
What to be found:
find the lcm of 45 and 64
step 2 Find the prime factors of 45 and 64:
Prime factors of 45 = 3 x 3 x 5
Prime factors of 64 = 2 x 2 x 2 x 2 x 2 x 2
step 3Identify the repeated and non-repeated prime factors of 45 and 64:
Since there is no common factors between 45 and 64, multiplying the given numbers directly provides the LCM of
45 and 64.
= 45 x 64
= 2880
lcm(45 and 64) = 2880
Hence,
lcm of 45 and 64 is 2880
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 45 and 64.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 45 and 64
What to be found:
lcm (45, 64) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
45 and 64
step 3 Choose the divisor which divides each or most of the given integers (45 and 64), 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 45 and 64 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 45 | 64 |
| 2 | 45 | 32 |
| 2 | 45 | 16 |
| 2 | 45 | 8 |
| 2 | 45 | 4 |
| 2 | 45 | 2 |
| 3 | 45 | 1 |
| 3 | 15 | 1 |
| 5 | 5 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 45 and 64:
= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
= 2880
LCM(45, 64) = 2880
The LCM of two numbers 45 and 64 is 2880