LCM of 152 and 234
17784 is the LCM of 152 and 234. 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 152 and 234, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 152 and 234?
lcm (152 234) = (?)
152 => 2 x 2 x 2 x 19
234 => 2 x 3 x 3 x 13
= 2 x 2 x 2 x 19 x 3 x 3 x 13
= 17784
lcm (152 and 234) = 17784
17784 is the LCM of 152 and 234.
where,
152 is a positive integer,
234 is a positive integer,
17784 is the LCM of 152 and 234,
{2} in {2 x 2 x 2 x 19, 2 x 3 x 3 x 13} is the common factors of 152 and 234,
{2 x 2 x 19 x 3 x 3 x 13} in {2 x 2 x 2 x 19, 2 x 3 x 3 x 13} are the uncommon factors of 152 and 234.
Use in Mathematics: LCM of 152 and 234
The below are some of the mathematical applications where lcm of 152 and 234 can be used:
- to find the least number which is exactly divisible by 152 and 234.
- to find the common denominator for two fractions having 152 and 234 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 152 and 234 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 152 seconds and bell B tolls at 234 seconds repeatedly. The answer is that all bells A and B toll together at 17784 seconds for the first time, at 35568 seconds for the second time, at 53352 seconds for the third time and so on.
Important Notes: 152 and 234 lcm
The below are the important notes to be remembered while solving the lcm of 152 and 234:
- The common prime factors and the remaining prime factors of 152 and 234 should be multiplied to find the least common multiple of 152 and 234, when solving lcm by using prime factors method.
- The results of lcm of 152 and 234, and the lcm of 234 and 152 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 152 and 234?
The below solved example with step by step work shows how to find what is the lcm of 152 and 234 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 152 and 234?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 152
B = 234
What to be found:
find the lcm of 152 and 234
step 2 Find the prime factors of 152 and 234:
Prime factors of 152 = 2 x 2 x 2 x 19
Prime factors of 234 = 2 x 3 x 3 x 13
step 3 Identify the repeated and non-repeated prime factors of 152 and 234:
{2} is the most repeated factor and {2 x 2 x 19 x 3 x 3 x 13} are the non-repeated factors of 152 and 234.
step 4 Find the product of repeated and non-repeated prime factors of 152 and 234:
= 2 x 2 x 2 x 19 x 3 x 3 x 13
= 17784
lcm(152 and 234) = 17784
Hence,
lcm of 152 and 234 is 17784
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 152 and 234.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 152 and 234
What to be found:
lcm (152, 234) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
152 and 234
step 3 Choose the divisor which divides each or most of the given integers (152 and 234), 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 152 and 234 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 152 | 234 |
| 2 | 76 | 117 |
| 2 | 38 | 117 |
| 3 | 19 | 117 |
| 3 | 19 | 39 |
| 13 | 19 | 13 |
| 19 | 19 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 152 and 234:
= 2 x 2 x 2 x 3 x 3 x 13 x 19
= 17784
LCM(152, 234) = 17784
The LCM of two numbers 152 and 234 is 17784