LCM of 70 and 336
1680 is the LCM of 70 and 336. 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 70 and 336, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 70 and 336?
lcm (70 336) = (?)
70 => 2 x 5 x 7
336 => 2 x 2 x 2 x 2 x 3 x 7
= 2 x 7 x 5 x 2 x 2 x 2 x 3
= 1680
lcm (70 and 336) = 1680
1680 is the LCM of 70 and 336.
where,
70 is a positive integer,
336 is a positive integer,
1680 is the LCM of 70 and 336,
{2 x 7} in {2 x 5 x 7, 2 x 2 x 2 x 2 x 3 x 7} are the common factors of 70 and 336,
{5 x 2 x 2 x 2 x 3} in {2 x 5 x 7, 2 x 2 x 2 x 2 x 3 x 7} are the uncommon factors of 70 and 336.
Use in Mathematics: LCM of 70 and 336
The below are some of the mathematical applications where lcm of 70 and 336 can be used:
- to find the least number which is exactly divisible by 70 and 336.
- to find the common denominator for two fractions having 70 and 336 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 70 and 336 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 70 seconds and bell B tolls at 336 seconds repeatedly. The answer is that all bells A and B toll together at 1680 seconds for the first time, at 3360 seconds for the second time, at 5040 seconds for the third time and so on.
Important Notes: 70 and 336 lcm
The below are the important notes to be remembered while solving the lcm of 70 and 336:
- The common prime factors and the remaining prime factors of 70 and 336 should be multiplied to find the least common multiple of 70 and 336, when solving lcm by using prime factors method.
- The results of lcm of 70 and 336, and the lcm of 336 and 70 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 70 and 336?
The below solved example with step by step work shows how to find what is the lcm of 70 and 336 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 70 and 336?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 70
B = 336
What to be found:
find the lcm of 70 and 336
step 2 Find the prime factors of 70 and 336:
Prime factors of 70 = 2 x 5 x 7
Prime factors of 336 = 2 x 2 x 2 x 2 x 3 x 7
step 3 Identify the repeated and non-repeated prime factors of 70 and 336:
{2, 7} are the most repeated factors and {5 x 2 x 2 x 2 x 3} are the non-repeated factors of 70 and 336.
step 4 Find the product of repeated and non-repeated prime factors of 70 and 336:
= 2 x 7 x 5 x 2 x 2 x 2 x 3
= 1680
lcm(70 and 336) = 1680
Hence,
lcm of 70 and 336 is 1680
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 70 and 336.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 70 and 336
What to be found:
lcm (70, 336) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
70 and 336
step 3 Choose the divisor which divides each or most of the given integers (70 and 336), 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 70 and 336 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 70 | 336 |
| 2 | 35 | 168 |
| 2 | 35 | 84 |
| 2 | 35 | 42 |
| 3 | 35 | 21 |
| 5 | 35 | 7 |
| 7 | 7 | 7 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 70 and 336:
= 2 x 2 x 2 x 2 x 3 x 5 x 7
= 1680
LCM(70, 336) = 1680
The LCM of two numbers 70 and 336 is 1680