Answer:
LCM = 1440
Step-by-step explanation:
To find the Least Common Multiple (LCM) of 72, 96, and 120 using the division method, follow these steps:
Step 1: Write the numbers in a row and divide them by a common prime number that can divide at least two of the numbers.
Step 2: Write the quotients below each number. If a number is not divisible by the prime number, carry it down as it is.
Step 3: Repeat the process with the new set of numbers until all the numbers have been reduced to 1.
Here's how you can calculate it:
```
2 | 72 96 120
| ----------------
2 | 36 48 60
| ----------------
2 | 18 24 30
| ----------------
2 | 9 12 15
| ----------------
3 | 9 6 5
| ----------------
3 | 3 2 5
| ----------------
| 1 2 5
| ----------------
2 | 1 1 5
| ----------------
5 | 1 1 1
| ----------------
```
Now, multiply all the divisors used to get the LCM:
LCM = 2 × 2 \times 2 × 2 × 3 × 3 × 2 × 5 = 1440
So, the LCM of 72, 96, and 120 is 1440.
