# 34 and 51 LCM LCM of 34 and 51 is equal to 102. The comprehensive work provides more insight of how to find what is the lcm of 34 and 51 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

what is the lcm of 34 and 51?
lcm (34   51) = (?)
34 => 2 x 17
51 => 3 x 17

= 17 x 2 x 3
= 102
lcm (34 and 51) = 102
102 is the lcm of 34 and 51.

where,
34 is a positive integer,
51 is a positive integer,
102 is the lcm of 34 and 51,
{17} in {2 x 17, 3 x 17} is the common factors of 34 and 51,
{2 x 3} in {2 x 17, 3 x 17} are the uncommon factors of 34 and 51.

Use in Mathematics: LCM of 34 and 51
The below are some of the mathematical applications where lcm of 34 and 51 can be used:

1. to find the least number which is exactly divisible by 34 and 51.
2. to find the common denominator for two fractions having 34 and 51 as denominators in the unlike fractions addition or subtraction.
Use in Real-world Problems: 34 and 51 lcm
In the context of lcm real world problems, the lcm of 34 and 51 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 34 seconds and bell B tolls at 51 seconds repeatedly. The answer is that all bells A and B toll together at 102 seconds for the first time, at 204 seconds for the second time, at 306 seconds for the third time and so on.

Important Notes: 34 and 51 lcm
The below are the important notes to be remembered while solving the lcm of 34 and 51:
1. The common prime factors and the remaining prime factors of 34 and 51 should be multiplied to find the least common multiple of 34 and 51, when solving lcm by using prime factors method.
2. The results of lcm of 34 and 51, and the lcm of 51 and 34 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
For values other than 34 and 51, use this below tool:

## How-to: What is the LCM of 34 and 51?

The below solved example with step by step work shows how to find what is the lcm of 34 and 51 by using prime factors method and division method.

Solved example using prime factors method:
What is the LCM of 34 and 51?

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 34
B = 51

What to be found:
find the lcm of 34 and 51

step 2 Find the prime factors of 34 and 51:
Prime factors of 34 = 2 x 17
Prime factors of 51 = 3 x 17

step 3 Identify the repeated and non-repeated prime factors of 34 and 51:
{17} is the most repeated factor and {2 x 3} are the non-repeated factors of 34 and 51.

step 4 Find the product of repeated and non-repeated prime factors of 34 and 51:
= 17 x 2 x 3
= 102
lcm(34 and 51) = 102

Hence,
lcm of 34 and 51 is 102

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 34 and 51.

step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 34 and 51

What to be found:
lcm (34, 51) = ?

step 2 Arrange the given integers in the horizontal form with space or comma separated format:
34 and 51

step 3 Choose the divisor which divides each or most of the given integers (34 and 51), 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 34 and 51 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:

 2 34 51 3 17 51 17 17 17 1 1

step 4 Multiply the divisors to find the lcm of 34 and 51:
= 2 x 3 x 17
= 102
LCM(34, 51) = 102

The least common multiple for two numbers 34 and 51 is 102 