LCM of 60 and 104
1560 is the LCM of 60 and 104. 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 60 and 104, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 60 and 104?
lcm (60 104) = (?)
60 => 2 x 2 x 3 x 5
104 => 2 x 2 x 2 x 13
= 2 x 2 x 3 x 5 x 2 x 13
= 1560
lcm (60 and 104) = 1560
1560 is the LCM of 60 and 104.
where,
60 is a positive integer,
104 is a positive integer,
1560 is the LCM of 60 and 104,
{2 x 2} in {2 x 2 x 3 x 5, 2 x 2 x 2 x 13} are the common factors of 60 and 104,
{3 x 5 x 2 x 13} in {2 x 2 x 3 x 5, 2 x 2 x 2 x 13} are the uncommon factors of 60 and 104.
Use in Mathematics: LCM of 60 and 104
The below are some of the mathematical applications where lcm of 60 and 104 can be used:
- to find the least number which is exactly divisible by 60 and 104.
- to find the common denominator for two fractions having 60 and 104 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 60 and 104 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 60 seconds and bell B tolls at 104 seconds repeatedly. The answer is that all bells A and B toll together at 1560 seconds for the first time, at 3120 seconds for the second time, at 4680 seconds for the third time and so on.
Important Notes: 60 and 104 lcm
The below are the important notes to be remembered while solving the lcm of 60 and 104:
- The common prime factors and the remaining prime factors of 60 and 104 should be multiplied to find the least common multiple of 60 and 104, when solving lcm by using prime factors method.
- The results of lcm of 60 and 104, and the lcm of 104 and 60 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 60 and 104?
The below solved example with step by step work shows how to find what is the lcm of 60 and 104 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 60 and 104?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 60
B = 104
What to be found:
find the lcm of 60 and 104
step 2 Find the prime factors of 60 and 104:
Prime factors of 60 = 2 x 2 x 3 x 5
Prime factors of 104 = 2 x 2 x 2 x 13
step 3 Identify the repeated and non-repeated prime factors of 60 and 104:
{2, 2} are the most repeated factors and {3 x 5 x 2 x 13} are the non-repeated factors of 60 and 104.
step 4 Find the product of repeated and non-repeated prime factors of 60 and 104:
= 2 x 2 x 3 x 5 x 2 x 13
= 1560
lcm(60 and 104) = 1560
Hence,
lcm of 60 and 104 is 1560
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 60 and 104.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 60 and 104
What to be found:
lcm (60, 104) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
60 and 104
step 3 Choose the divisor which divides each or most of the given integers (60 and 104), 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 60 and 104 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 60 | 104 |
| 2 | 30 | 52 |
| 2 | 15 | 26 |
| 3 | 15 | 13 |
| 5 | 5 | 13 |
| 13 | 1 | 13 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 60 and 104:
= 2 x 2 x 2 x 3 x 5 x 13
= 1560
LCM(60, 104) = 1560
The LCM of two numbers 60 and 104 is 1560