LCM of 45, 50 and 105
3150 is the LCM of 45, 50 and 105. 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, 50 and 105, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 45, 50 and 105?
lcm (45 50 105) = (?)
45 => 3 x 3 x 5
50 => 2 x 5 x 5
105 => 3 x 5 x 7
= 3 x 5 x 3 x 2 x 5 x 7
= 3150
lcm (45, 50 and 105) = 3150
The LCM of 45, 50 and 105 is 3150
where,
45 is a positive integer,
50 is a positive integer,
3150 is the LCM of 45, 50 and 105,
{3, 5} in {3 x 3 x 5, 2 x 5 x 5, 3 x 5 x 7} are the most repeated factors of 45, 50 and 105,
{3, 2, 5, 7} in {3 x 3 x 5, 2 x 5 x 5, 3 x 5 x 7} are the the other remaining factors of 45, 50 and 105.
Use in Mathematics: LCM of 45, 50 and 105
The below are some of the mathematical applications where lcm of 45, 50 and 105 can be used:
- to find the least number which is exactly divisible by 45, 50 and 105.
- to find the common denominators for the fractions having 45, 50 and 105 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 45, 50 and 105 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 45 seconds, B tolls at 50 seconds and C tolls at 105 seconds repeatedly. The answer is that all bells A, B and C toll together at 3150 seconds for the first time, at 6300 seconds for the second time, at 9450 seconds for the third time and so on.
Important Notes: 45, 50 and 105 lcm
The below are the important notes to be remembered while solving the lcm of 45, 50 and 105:
- The repeated and non-repeated prime factors of 45, 50 and 105 should be multiplied to find the least common multiple of 45, 50 and 105, when solving lcm by using prime factors method.
- The results of lcm of 45, 50 and 105 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 LCM of 45, 50 and 105?
The below solved example with step by step work shows how to find what is the lcm of 45, 50 and 105 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 45, 50 and 105?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 45
B = 50
C = 105
What to be found:
Find lcm of 45, 50 and 105
step 2 Find the prime factors of 45, 50 and 105:
Prime factors of 45 = 3 x 3 x 5
Prime factors of 50 = 2 x 5 x 5
Prime factors of 105 = 3 x 5 x 7
step 3 Identify the repeated and non-repeated prime factors of 45, 50 and 105:
{3, 5} are the most repeated factors and {3, 2, 5, 7} are the non-repeated factors of 45, 50 and 105.
step 4 Find the product of repeated and non-repeated prime factors of 45, 50 and 105:
= 3 x 5 x 3 x 2 x 5 x 7
= 3150
LCM(45, 50 and 105) = 3150
Hence,
The Least Common Multiple of 45, 50 and 105 is 3150
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 45, 50 and 105.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 45, 50 and 105
What to be found:
lcm (45, 50, 105) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
45, 50 and 105
step 3 Choose the divisor which divides each or most of the given integers (45, 50 and 105), 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, 50 and 105 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 45 | 50 | 105 |
| 3 | 45 | 25 | 105 |
| 3 | 15 | 25 | 35 |
| 5 | 5 | 25 | 35 |
| 5 | 1 | 5 | 7 |
| 7 | 1 | 1 | 7 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 45, 50 and 105:
= 2 x 3 x 3 x 5 x 5 x 7
= 3150
LCM(45, 50, 105) = 3150
The LCM of three numbers 45, 50 and 105 is 3150