LCM of 10 and 14
70 is the LCM of 10 and 14. 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 10 and 14, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 10 and 14?
lcm (10 14) = (?)
10 => 2 x 5
14 => 2 x 7
= 2 x 5 x 7
= 70
lcm (10 and 14) = 70
70 is the LCM of 10 and 14.
where,
10 is a positive integer,
14 is a positive integer,
70 is the LCM of 10 and 14,
{2} in {2 x 5, 2 x 7} is the common factors of 10 and 14,
{5 x 7} in {2 x 5, 2 x 7} are the uncommon factors of 10 and 14.
Use in Mathematics: LCM of 10 and 14
The below are some of the mathematical applications where lcm of 10 and 14 can be used:
- to find the least number which is exactly divisible by 10 and 14.
- to find the common denominator for two fractions having 10 and 14 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 10 and 14 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 10 seconds and bell B tolls at 14 seconds repeatedly. The answer is that all bells A and B toll together at 70 seconds for the first time, at 140 seconds for the second time, at 210 seconds for the third time and so on.
Important Notes: 10 and 14 lcm
The below are the important notes to be remembered while solving the lcm of 10 and 14:
- The common prime factors and the remaining prime factors of 10 and 14 should be multiplied to find the least common multiple of 10 and 14, when solving lcm by using prime factors method.
- The results of lcm of 10 and 14, and the lcm of 14 and 10 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 10 and 14?
The below solved example with step by step work shows how to find what is the lcm of 10 and 14 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 10 and 14?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 10
B = 14
What to be found:
find the lcm of 10 and 14
step 2 Find the prime factors of 10 and 14:
Prime factors of 10 = 2 x 5
Prime factors of 14 = 2 x 7
step 3 Identify the repeated and non-repeated prime factors of 10 and 14:
{2} is the most repeated factor and {5 x 7} are the non-repeated factors of 10 and 14.
step 4 Find the product of repeated and non-repeated prime factors of 10 and 14:
= 2 x 5 x 7
= 70
lcm(10 and 14) = 70
Hence,
lcm of 10 and 14 is 70
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 10 and 14.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 10 and 14
What to be found:
lcm (10, 14) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
10 and 14
step 3 Choose the divisor which divides each or most of the given integers (10 and 14), 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 10 and 14 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 10 | 14 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 10 and 14:
= 2 x 5 x 7
= 70
LCM(10, 14) = 70
The LCM of two numbers 10 and 14 is 70