1

Problem

Find the least common multiple for the following numbers:
20 and 80.

2

Step

The given numbers are

20 and 80

3

Hint

To find the least common multiple (LCM) of 20 and 80, you can use the prime factorization method.

4

Step

Prime factorization of 20:

\$ 2^2 \times 5^1\$

5

Step

Prime factorization of 80:

\$ 2^4 \times 5^1 \$

6

Step

Next, we identify the highest powers of each prime factor. So the highest power of 2 is:

\$ 2^4 \$

7

Step

The highest power of 5 is:

\$ 5^1 \$

8

Step

Multiply the highest powers of each prime factor together:

\$ "LCM" = (2)^4 \times (5)^1\$

9

Step

After simplification:

\$ "LCM" = 16 \times 5 \$
LCM = 80

10

Solution

Finally, the result of the least common multiple is 80.

11

Sumup

Please summarize steps

Choices

12

Choice-A

40 is not a multiple of 80, as 80 is the smallest multiple that both 20 and 80 share. This choice is wrong

Wrong 40

13

Choice-B

This is incorrect because 16 is not a multiple of both 20 and 80

Wrong 16

14

Choice-C

20 is not a common multiple of both 20 and 80 because 80 is a multiple of 20, but 20 is not a multiple of 80. So, this is incorrect

Wrong 20

15

Choice-D

This is correct because 80 is the least common multiple of 20 and 80

Correct 80

16

Step

Option

D

17

Sumup

Please summarize choices