LCM of 60 and 189
3780 is the LCM of 60 and 189. 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 189, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 60 and 189?
lcm (60 189) = (?)
60 => 2 x 2 x 3 x 5
189 => 3 x 3 x 3 x 7
= 3 x 2 x 2 x 5 x 3 x 3 x 7
= 3780
lcm (60 and 189) = 3780
3780 is the LCM of 60 and 189.
where,
60 is a positive integer,
189 is a positive integer,
3780 is the LCM of 60 and 189,
{3} in {2 x 2 x 3 x 5, 3 x 3 x 3 x 7} is the common factors of 60 and 189,
{2 x 2 x 5 x 3 x 3 x 7} in {2 x 2 x 3 x 5, 3 x 3 x 3 x 7} are the uncommon factors of 60 and 189.
Use in Mathematics: LCM of 60 and 189
The below are some of the mathematical applications where lcm of 60 and 189 can be used:
- to find the least number which is exactly divisible by 60 and 189.
- to find the common denominator for two fractions having 60 and 189 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 60 and 189 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 189 seconds repeatedly. The answer is that all bells A and B toll together at 3780 seconds for the first time, at 7560 seconds for the second time, at 11340 seconds for the third time and so on.
Important Notes: 60 and 189 lcm
The below are the important notes to be remembered while solving the lcm of 60 and 189:
- The common prime factors and the remaining prime factors of 60 and 189 should be multiplied to find the least common multiple of 60 and 189, when solving lcm by using prime factors method.
- The results of lcm of 60 and 189, and the lcm of 189 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 189?
The below solved example with step by step work shows how to find what is the lcm of 60 and 189 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 60 and 189?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 60
B = 189
What to be found:
find the lcm of 60 and 189
step 2 Find the prime factors of 60 and 189:
Prime factors of 60 = 2 x 2 x 3 x 5
Prime factors of 189 = 3 x 3 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 60 and 189:
{3} is the most repeated factor and {2 x 2 x 5 x 3 x 3 x 7} are the non-repeated factors of 60 and 189.
step 4 Find the product of repeated and non-repeated prime factors of 60 and 189:
= 3 x 2 x 2 x 5 x 3 x 3 x 7
= 3780
lcm(60 and 189) = 3780
Hence,
lcm of 60 and 189 is 3780
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 60 and 189.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 60 and 189
What to be found:
lcm (60, 189) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
60 and 189
step 3 Choose the divisor which divides each or most of the given integers (60 and 189), 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 189 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 60 | 189 |
| 2 | 30 | 189 |
| 3 | 15 | 189 |
| 3 | 5 | 63 |
| 3 | 5 | 21 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 60 and 189:
= 2 x 2 x 3 x 3 x 3 x 5 x 7
= 3780
LCM(60, 189) = 3780
The LCM of two numbers 60 and 189 is 3780