LCM of 34 and 61
2074 is the LCM of 34 and 61. 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 34 and 61, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 34 and 61?
lcm (34 61) = (?)
34 => 2 x 17
61 => 61
= 2 x 17 x 61
= 2074
lcm (34 and 61) = 2074
2074 is the LCM of 34 and 61.
where,
34 is a positive integer,
61 is a positive integer,
2074 is the LCM of 34 and 61,
There is no common factors of 34 and 61 in {2 x 17, 61},
{2 x 17 x 61} in {2 x 17, 61} are the uncommon factors of 34 and 61.
Use in Mathematics: LCM of 34 and 61
The below are some of the mathematical applications where lcm of 34 and 61 can be used:
- to find the least number which is exactly divisible by 34 and 61.
- to find the common denominator for two fractions having 34 and 61 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 34 and 61 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 34 seconds and bell B tolls at 61 seconds repeatedly. The answer is that all bells A and B toll together at 2074 seconds for the first time, at 4148 seconds for the second time, at 6222 seconds for the third time and so on.
Important Notes: 34 and 61 lcm
The below are the important notes to be remembered while solving the lcm of 34 and 61:
- The common prime factors and the remaining prime factors of 34 and 61 should be multiplied to find the least common multiple of 34 and 61, when solving lcm by using prime factors method.
- The results of lcm of 34 and 61, and the lcm of 61 and 34 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 34 and 61?
The below solved example with step by step work shows how to find what is the lcm of 34 and 61 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 34 and 61?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 34
B = 61
What to be found:
find the lcm of 34 and 61
step 2 Find the prime factors of 34 and 61:
Prime factors of 34 = 2 x 17
Prime factors of 61 = 61
step 3Identify the repeated and non-repeated prime factors of 34 and 61:
Since there is no common factors between 34 and 61, multiplying the given numbers directly provides the LCM of
34 and 61.
= 34 x 61
= 2074
lcm(34 and 61) = 2074
Hence,
lcm of 34 and 61 is 2074
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 34 and 61.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 34 and 61
What to be found:
lcm (34, 61) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
34 and 61
step 3 Choose the divisor which divides each or most of the given integers (34 and 61), 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 34 and 61 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 34 | 61 |
| 17 | 17 | 61 |
| 61 | 1 | 61 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 34 and 61:
= 2 x 17 x 61
= 2074
LCM(34, 61) = 2074
The LCM of two numbers 34 and 61 is 2074