LCM of 60, 65 and 77
60060 is the LCM of 60, 65 and 77. 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, 65 and 77, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 60, 65 and 77?
lcm (60 65 77) = (?)
60 => 2 x 2 x 3 x 5
65 => 5 x 13
77 => 7 x 11
= 5 x 2 x 2 x 3 x 13 x 7 x 11
= 60060
lcm (60, 65 and 77) = 60060
The LCM of 60, 65 and 77 is 60060
where,
60 is a positive integer,
65 is a positive integer,
60060 is the LCM of 60, 65 and 77,
{5} in {2 x 2 x 3 x 5, 5 x 13, 7 x 11} is the most repeated factors of 60, 65 and 77,
{2, 2, 3, 13, 7, 11} in {2 x 2 x 3 x 5, 5 x 13, 7 x 11} are the the other remaining factors of 60, 65 and 77.
Use in Mathematics: LCM of 60, 65 and 77
The below are some of the mathematical applications where lcm of 60, 65 and 77 can be used:
- to find the least number which is exactly divisible by 60, 65 and 77.
- to find the common denominators for the fractions having 60, 65 and 77 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 60, 65 and 77 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 60 seconds, B tolls at 65 seconds and C tolls at 77 seconds repeatedly. The answer is that all bells A, B and C toll together at 60060 seconds for the first time, at 120120 seconds for the second time, at 180180 seconds for the third time and so on.
Important Notes: 60, 65 and 77 lcm
The below are the important notes to be remembered while solving the lcm of 60, 65 and 77:
- The repeated and non-repeated prime factors of 60, 65 and 77 should be multiplied to find the least common multiple of 60, 65 and 77, when solving lcm by using prime factors method.
- The results of lcm of 60, 65 and 77 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 60, 65 and 77?
The below solved example with step by step work shows how to find what is the lcm of 60, 65 and 77 by using either prime factors method and special division method.
Solved example using prime factors method:
What is LCM of 60, 65 and 77?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 60
B = 65
C = 77
What to be found:
Find lcm of 60, 65 and 77
step 2 Find the prime factors of 60, 65 and 77:
Prime factors of 60 = 2 x 2 x 3 x 5
Prime factors of 65 = 5 x 13
Prime factors of 77 = 7 x 11
step 3 Identify the repeated and non-repeated prime factors of 60, 65 and 77:
{5} is the most repeated factor and {2, 2, 3, 13, 7, 11} are the non-repeated factors of 60, 65 and 77.
step 4 Find the product of repeated and non-repeated prime factors of 60, 65 and 77:
= 5 x 2 x 2 x 3 x 13 x 7 x 11
= 60060
LCM(60, 65 and 77) = 60060
Hence,
The Least Common Multiple of 60, 65 and 77 is 60060
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 60, 65 and 77.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 60, 65 and 77
What to be found:
lcm (60, 65, 77) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
60, 65 and 77
step 3 Choose the divisor which divides each or most of the given integers (60, 65 and 77), 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, 65 and 77 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 60 | 65 | 77 |
| 2 | 30 | 65 | 77 |
| 3 | 15 | 65 | 77 |
| 5 | 5 | 65 | 77 |
| 7 | 1 | 13 | 77 |
| 11 | 1 | 13 | 11 |
| 13 | 1 | 13 | 1 |
| 1 | 1 | 1 |
step 4 Multiply the divisors to find the lcm of 60, 65 and 77:
= 2 x 2 x 3 x 5 x 7 x 11 x 13
= 60060
LCM(60, 65, 77) = 60060
The LCM of three numbers 60, 65 and 77 is 60060