Question

find the LCM of prime factorization method of 11558, 2054,33240
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Answer 1

In this problem, we are assuming that we have to find the LCM of the given data.

Q. Find LCM of the numbers$11558, 2054,33240$ by the prime factorization method.

Given: The numbers are$11558, 2054,33240$.

We have to find the LCM of the above numbers.

We are solving in the following way:

We have,

The numbers are$11558, 2054,33240$.

First, we will list all prime factors for each number.

Prime Factorization of 2054 is:

$2 \times 13 \times 79 => 2^1 \times 13^1 \times 79^1$

Prime Factorization of 11558 is:

$2 \times 5779 => 2^1 \times 5779^1$

Prime Factorization of 33240 is:

$2 \times 2 \times 2 \times 3 \times 5 \times 277 => 2^3 \times 3^1 \times 5^1 \times 277^1$

For each prime factor, we will find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

$2, 2, 2, 3, 5, 13, 79, 277, 5779$

Multiplying these factors together to find the LCM.

$LCM = 2 \times 2 \times2 \times 3 \times 5 \times 13 \times 79 \times277 \times 5779 = 197280496920$

Therefore,

$LCM(2054, 11558, 33240) = 197,280,496,920$

Hence, we get $LCM = 197,280,496,920$