LCM of 77 and 316
24332 is the LCM of 77 and 316. 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 77 and 316, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 77 and 316?
lcm (77 316) = (?)
77 => 7 x 11
316 => 2 x 2 x 79
= 7 x 11 x 2 x 2 x 79
= 24332
lcm (77 and 316) = 24332
24332 is the LCM of 77 and 316.
where,
77 is a positive integer,
316 is a positive integer,
24332 is the LCM of 77 and 316,
There is no common factors of 77 and 316 in {7 x 11, 2 x 2 x 79},
{7 x 11 x 2 x 2 x 79} in {7 x 11, 2 x 2 x 79} are the uncommon factors of 77 and 316.
Use in Mathematics: LCM of 77 and 316
The below are some of the mathematical applications where lcm of 77 and 316 can be used:
- to find the least number which is exactly divisible by 77 and 316.
- to find the common denominator for two fractions having 77 and 316 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 77 and 316 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 77 seconds and bell B tolls at 316 seconds repeatedly. The answer is that all bells A and B toll together at 24332 seconds for the first time, at 48664 seconds for the second time, at 72996 seconds for the third time and so on.
Important Notes: 77 and 316 lcm
The below are the important notes to be remembered while solving the lcm of 77 and 316:
- The common prime factors and the remaining prime factors of 77 and 316 should be multiplied to find the least common multiple of 77 and 316, when solving lcm by using prime factors method.
- The results of lcm of 77 and 316, and the lcm of 316 and 77 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 77 and 316?
The below solved example with step by step work shows how to find what is the lcm of 77 and 316 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 77 and 316?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 77
B = 316
What to be found:
find the lcm of 77 and 316
step 2 Find the prime factors of 77 and 316:
Prime factors of 77 = 7 x 11
Prime factors of 316 = 2 x 2 x 79
step 3Identify the repeated and non-repeated prime factors of 77 and 316:
Since there is no common factors between 77 and 316, multiplying the given numbers directly provides the LCM of
77 and 316.
= 77 x 316
= 24332
lcm(77 and 316) = 24332
Hence,
lcm of 77 and 316 is 24332
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 77 and 316.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 77 and 316
What to be found:
lcm (77, 316) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
77 and 316
step 3 Choose the divisor which divides each or most of the given integers (77 and 316), 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 77 and 316 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 77 | 316 |
| 2 | 77 | 158 |
| 7 | 77 | 79 |
| 11 | 11 | 79 |
| 79 | 1 | 79 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 77 and 316:
= 2 x 2 x 7 x 11 x 79
= 24332
LCM(77, 316) = 24332
The LCM of two numbers 77 and 316 is 24332