12 and 90 LCM
LCM of 12 and 90 is equal to 180. The comprehensive work provides more insight of how to find what is the lcm of 12 and 90 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 12 and 90?
lcm (12 90) = (?)
12 => 2 x 2 x 3
90 => 2 x 3 x 3 x 5
= 2 x 3 x 2 x 3 x 5
= 180
lcm (12 and 90) = 180
180 is the lcm of 12 and 90.
where,
12 is a positive integer,
90 is a positive integer,
180 is the lcm of 12 and 90,
{2 x 3} in {2 x 2 x 3, 2 x 3 x 3 x 5} are the common factors of 12 and 90,
{2 x 3 x 5} in {2 x 2 x 3, 2 x 3 x 3 x 5} are the uncommon factors of 12 and 90.
Use in Mathematics: LCM of 12 and 90
The below are some of the mathematical applications where lcm of 12 and 90 can be used:
- to find the least number which is exactly divisible by 12 and 90.
- to find the common denominator for two fractions having 12 and 90 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 12 and 90 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 12 seconds and bell B tolls at 90 seconds repeatedly. The answer is that all bells A and B toll together at 180 seconds for the first time, at 360 seconds for the second time, at 540 seconds for the third time and so on.
Important Notes: 12 and 90 lcm
The below are the important notes to be remembered while solving the lcm of 12 and 90:
- The common prime factors and the remaining prime factors of 12 and 90 should be multiplied to find the least common multiple of 12 and 90, when solving lcm by using prime factors method.
- The results of lcm of 12 and 90, and the lcm of 90 and 12 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 12 and 90, use this below tool:
How-to: What is the LCM of 12 and 90?
The below solved example with step by step work shows how to find what is the lcm of 12 and 90 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 12 and 90?
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 90
What to be found:
find the lcm of 12 and 90
step 2 Find the prime factors of 12 and 90:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 90 = 2 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 12 and 90:
{2, 3} are the most repeated factors and {2 x 3 x 5} are the non-repeated factors of 12 and 90.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 90:
= 2 x 3 x 2 x 3 x 5
= 180
lcm(12 and 90) = 180
Hence,
lcm of 12 and 90 is 180
Solved example using prime factors method:
What is the LCM of 12 and 90?
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 12
B = 90
What to be found:
find the lcm of 12 and 90
step 2 Find the prime factors of 12 and 90:
Prime factors of 12 = 2 x 2 x 3
Prime factors of 90 = 2 x 3 x 3 x 5
step 3 Identify the repeated and non-repeated prime factors of 12 and 90:
{2, 3} are the most repeated factors and {2 x 3 x 5} are the non-repeated factors of 12 and 90.
step 4 Find the product of repeated and non-repeated prime factors of 12 and 90:
= 2 x 3 x 2 x 3 x 5
= 180
lcm(12 and 90) = 180
Hence,
lcm of 12 and 90 is 180
Solved example using special division method:
This special division method is the easiest way to understand the entire calculation of what is the lcm of 12 and 90.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 90
What to be found:
lcm (12, 90) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 90
step 3 Choose the divisor which divides each or most of the given integers (12 and 90), 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 12 and 90 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
step 4 Multiply the divisors to find the lcm of 12 and 90:
= 2 x 2 x 3 x 3 x 5
= 180
LCM(12, 90) = 180
The least common multiple for two numbers 12 and 90 is 180
This special division method is the easiest way to understand the entire calculation of what is the lcm of 12 and 90.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 12 and 90
What to be found:
lcm (12, 90) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
12 and 90
step 3 Choose the divisor which divides each or most of the given integers (12 and 90), 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 12 and 90 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 12 | 90 |
| 2 | 6 | 45 |
| 3 | 3 | 45 |
| 3 | 1 | 15 |
| 5 | 1 | 5 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 12 and 90:
= 2 x 2 x 3 x 3 x 5
= 180
LCM(12, 90) = 180
The least common multiple for two numbers 12 and 90 is 180
