Question

Find LCM: 13, 26 and 29.

Answer 1

Hint: Given are the three numbers whose LCM is to be found. We will use the prime factorization method here to find the LCM of the given numbers above. This uses only prime numbers which are written in product form to get the number. Then we take the common factor once and then the remaining factors whose product is the LCM itself.

Complete step-by-step answer:
Given the numbers are 13, 26 and 29.
Now if we notice that 13 and 29 are the prime numbers itself. So we can write the numbers as,
13=13
29=29
But 26 is not prime. It is the only composite number. So let’s write it in prime factor product form.
\[26 = 13 \times 2\]
Now there is no common factor for all the three numbers. So we will take all the numbers or factors as uncommon for finding the LCM
\[LCM = 13 \times 29 \times 2\]
On multiplying we get,
\[LCM = 754\]
Thus the LCM of 13, 26 and 29 is 754.
So, the correct answer is “754”.

Note: Note that there are other methods also to calculate the LCM like listing common multiples and then finding the lowest one.
Another method is using the grid and ladder method in which we make a grid form with the help of lines and write the numbers in uppermost grids. Then find a prime number that can commonly divide the numbers above. And write the quotient in the next grid below. This continues until all the numbers on dividing are not prime. And then the numbers in the lower most row and leftmost column, like forming L are taken into the product to get LCM.