Question

find the LCM of 36,54,72

Answer 1

36     = 2*2*3*3
54     = 2*3*3*3
72     = 2*2*2*3*3
LCM = 2*3*3*2*3*2*2
         = 432
          

Answer 2

Answer:

The lcm of 36, 54, and 72 is 216.

Explanation:

Given: The numbers are 36, 54, and 72​.

We have to find the lcm of the above numbers.

• As we know, LCM denotes the least common factor or multiple of any two or more given integers.  

We are solving in the following way:

We have,

The numbers are 36, 54, and 72​.

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

Prime Factorization of 36 is:

$2 \times 2 \times 3 \times 3 => 2^2 \times 3^2$

Prime Factorization of 54 is:

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

Prime Factorization of 72 is:

$2 \times 2 \times 2 \times 3 \times 3 => 2^3 \times 3^2$

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 list is:

2, 2, 2, 3, 3, 3

Multiplying these factors together to find the LCM:

$LCM = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 216$

Therefore,

LCM(36, 54, 72) = 216