LCM of 45 and 46
2070 is the LCM of 45 and 46. 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 46, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 45 and 46?
lcm (45 46) = (?)
45 => 3 x 3 x 5
46 => 2 x 23
= 3 x 3 x 5 x 2 x 23
= 2070
lcm (45 and 46) = 2070
2070 is the LCM of 45 and 46.
where,
45 is a positive integer,
46 is a positive integer,
2070 is the LCM of 45 and 46,
There is no common factors of 45 and 46 in {3 x 3 x 5, 2 x 23},
{3 x 3 x 5 x 2 x 23} in {3 x 3 x 5, 2 x 23} are the uncommon factors of 45 and 46.
Use in Mathematics: LCM of 45 and 46
The below are some of the mathematical applications where lcm of 45 and 46 can be used:
- to find the least number which is exactly divisible by 45 and 46.
- to find the common denominator for two fractions having 45 and 46 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 45 and 46 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 46 seconds repeatedly. The answer is that all bells A and B toll together at 2070 seconds for the first time, at 4140 seconds for the second time, at 6210 seconds for the third time and so on.
Important Notes: 45 and 46 lcm
The below are the important notes to be remembered while solving the lcm of 45 and 46:
- The common prime factors and the remaining prime factors of 45 and 46 should be multiplied to find the least common multiple of 45 and 46, when solving lcm by using prime factors method.
- The results of lcm of 45 and 46, and the lcm of 46 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 46?
The below solved example with step by step work shows how to find what is the lcm of 45 and 46 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 45 and 46?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 45
B = 46
What to be found:
find the lcm of 45 and 46
step 2 Find the prime factors of 45 and 46:
Prime factors of 45 = 3 x 3 x 5
Prime factors of 46 = 2 x 23
step 3Identify the repeated and non-repeated prime factors of 45 and 46:
Since there is no common factors between 45 and 46, multiplying the given numbers directly provides the LCM of
45 and 46.
= 45 x 46
= 2070
lcm(45 and 46) = 2070
Hence,
lcm of 45 and 46 is 2070
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 45 and 46.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 45 and 46
What to be found:
lcm (45, 46) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
45 and 46
step 3 Choose the divisor which divides each or most of the given integers (45 and 46), 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 46 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 45 | 46 |
| 3 | 45 | 23 |
| 3 | 15 | 23 |
| 5 | 5 | 23 |
| 23 | 1 | 23 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 45 and 46:
= 2 x 3 x 3 x 5 x 23
= 2070
LCM(45, 46) = 2070
The LCM of two numbers 45 and 46 is 2070