LCM of 68 and 119
476 is the LCM of 68 and 119. 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 68 and 119, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 68 and 119?
lcm (68 119) = (?)
68 => 2 x 2 x 17
119 => 7 x 17
= 17 x 2 x 2 x 7
= 476
lcm (68 and 119) = 476
476 is the LCM of 68 and 119.
where,
68 is a positive integer,
119 is a positive integer,
476 is the LCM of 68 and 119,
{17} in {2 x 2 x 17, 7 x 17} is the common factors of 68 and 119,
{2 x 2 x 7} in {2 x 2 x 17, 7 x 17} are the uncommon factors of 68 and 119.
Use in Mathematics: LCM of 68 and 119
The below are some of the mathematical applications where lcm of 68 and 119 can be used:
- to find the least number which is exactly divisible by 68 and 119.
- to find the common denominator for two fractions having 68 and 119 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 68 and 119 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 68 seconds and bell B tolls at 119 seconds repeatedly. The answer is that all bells A and B toll together at 476 seconds for the first time, at 952 seconds for the second time, at 1428 seconds for the third time and so on.
Important Notes: 68 and 119 lcm
The below are the important notes to be remembered while solving the lcm of 68 and 119:
- The common prime factors and the remaining prime factors of 68 and 119 should be multiplied to find the least common multiple of 68 and 119, when solving lcm by using prime factors method.
- The results of lcm of 68 and 119, and the lcm of 119 and 68 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 68 and 119?
The below solved example with step by step work shows how to find what is the lcm of 68 and 119 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 68 and 119?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 68
B = 119
What to be found:
find the lcm of 68 and 119
step 2 Find the prime factors of 68 and 119:
Prime factors of 68 = 2 x 2 x 17
Prime factors of 119 = 7 x 17
step 3 Identify the repeated and non-repeated prime factors of 68 and 119:
{17} is the most repeated factor and {2 x 2 x 7} are the non-repeated factors of 68 and 119.
step 4 Find the product of repeated and non-repeated prime factors of 68 and 119:
= 17 x 2 x 2 x 7
= 476
lcm(68 and 119) = 476
Hence,
lcm of 68 and 119 is 476
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 68 and 119.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 68 and 119
What to be found:
lcm (68, 119) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
68 and 119
step 3 Choose the divisor which divides each or most of the given integers (68 and 119), 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 68 and 119 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 68 | 119 |
| 2 | 34 | 119 |
| 7 | 17 | 119 |
| 17 | 17 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 68 and 119:
= 2 x 2 x 7 x 17
= 476
LCM(68, 119) = 476
The LCM of two numbers 68 and 119 is 476