68 and 153 LCM
LCM of 68 and 153 is equal to 612. The comprehensive work provides more insight of how to find what is the lcm of 68 and 153 by using prime factors and special division methods, and the example use case of mathematics and real world problems.
what is the lcm of 68 and 153?
lcm (68 153) = (?)
68 => 2 x 2 x 17
153 => 3 x 3 x 17
= 17 x 2 x 2 x 3 x 3
= 612
lcm (68 and 153) = 612
612 is the lcm of 68 and 153.
where,
68 is a positive integer,
153 is a positive integer,
612 is the lcm of 68 and 153,
{17} in {2 x 2 x 17, 3 x 3 x 17} is the common factors of 68 and 153,
{2 x 2 x 3 x 3} in {2 x 2 x 17, 3 x 3 x 17} are the uncommon factors of 68 and 153.
Use in Mathematics: LCM of 68 and 153
The below are some of the mathematical applications where lcm of 68 and 153 can be used:
- to find the least number which is exactly divisible by 68 and 153.
- to find the common denominator for two fractions having 68 and 153 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 68 and 153 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 68 seconds and bell B tolls at 153 seconds repeatedly. The answer is that all bells A and B toll together at 612 seconds for the first time, at 1224 seconds for the second time, at 1836 seconds for the third time and so on.
Important Notes: 68 and 153 lcm
The below are the important notes to be remembered while solving the lcm of 68 and 153:
- The common prime factors and the remaining prime factors of 68 and 153 should be multiplied to find the least common multiple of 68 and 153, when solving lcm by using prime factors method.
- The results of lcm of 68 and 153, and the lcm of 153 and 68 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 68 and 153?
The below solved example with step by step work shows how to find what is the lcm of 68 and 153 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 68 and 153?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 68
B = 153
What to be found:
find the lcm of 68 and 153
step 2 Find the prime factors of 68 and 153:
Prime factors of 68 = 2 x 2 x 17
Prime factors of 153 = 3 x 3 x 17
step 3 Identify the repeated and non-repeated prime factors of 68 and 153:
{17} is the most repeated factor and {2 x 2 x 3 x 3} are the non-repeated factors of 68 and 153.
step 4 Find the product of repeated and non-repeated prime factors of 68 and 153:
= 17 x 2 x 2 x 3 x 3
= 612
lcm(68 and 153) = 612
Hence,
lcm of 68 and 153 is 612
This special division method is the easiest way to understand the entire calculation of what is the lcm of 68 and 153.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 68 and 153
What to be found:
lcm (68, 153) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
68 and 153
step 3 Choose the divisor which divides each or most of the given integers (68 and 153), 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 68 and 153 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 68 | 153 |
| 2 | 34 | 153 |
| 3 | 17 | 153 |
| 3 | 17 | 51 |
| 17 | 17 | 17 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 68 and 153:
= 2 x 2 x 3 x 3 x 17
= 612
LCM(68, 153) = 612
The least common multiple for two numbers 68 and 153 is 612