Find LCM by Division Method: 48, 72, 80

To find the LCM (Least Common Multiple) of the numbers 48, 72, and 80 using the division method, follow these steps:

1. Write the numbers in a row:
• 48
• 72
• 80
2. Divide the numbers by their smallest prime factor. In this case, we can start with 2:
• 48 ÷ 2 = 24
• 72 ÷ 2 = 36
• 80 ÷ 2 = 40
3. Write the results below:
• 24
• 36
• 40
4. Continue dividing by 2:
• 24 ÷ 2 = 12
• 36 ÷ 2 = 18
• 40 ÷ 2 = 20
5. Now, the results are:
• 12
• 18
• 20
6. We now divide by 2 one more time:
• 12 ÷ 2 = 6
• 18 ÷ 2 = 9
• 20 ÷ 2 = 10
7. Next, we take 3 (the next smallest prime number):
• 9 ÷ 3 = 3
• 10 stays the same.
8. Continuing with 3:
• 3 ÷ 3 = 1
9. At this point, we have:
• 1
• 10
10. Now, we take 5:
• 10 ÷ 5 = 2
11. Finally, we have:
• 1
• 2

Now, we can find the LCM by multiplying all the prime factors together, using the numbers we divided by:

LCM = 2 × 2 × 2 × 3 × 5 = 120

Thus, the Least Common Multiple of 48, 72, and 80 is 480.