1

Problem

Find the least common multiple:
23 and 21.

2

Step

The given numbers are

23 and 21

3

Hint

To find the least common multiple (LCM) of 23 and 21, you can use the prime factorization method.

4

Step

Prime factorization of 23:

\$ (23)^1\$

5

Step

Prime factorization of 21:

\$ 3^1 \times 7^1 \$

6

Step

Next, we identify the highest powers of each prime factor. So the highest power of 23 is:

\$ (23)^1 \$

7

Step

The highest power of 3 is:

\$ 3^1 \$

8

Step

The highest power of 7 is:

\$ 7^1 \$

9

Step

Multiply the highest powers of each prime factor together:

\$ "LCM" = (23)^1 \times 3^1 \times 7^1\$

10

Step

After simplification:

\$ "LCM" = 23 \times 3 \times 7 \$
LCM = 483

11

Solution

So, the least common multiple is 483.

12

Sumup

Please summarize steps

Choices

13

Choice-A

This is not the correct answer because 493 is not divisible by 21

Wrong 493

14

Choice-B

This is incorrect because it doesn’t meet the requirement of being a multiple of both numbers

Wrong 473

15

Choice-C

This is correct because it is the smallest common multiple of 23 and 21

Correct 483

16

Choice-D

This is not the correct answer because 463 is neither divisible by 23 nor by 21

Wrong 463

17

Step

Option

C

18

Sumup

Please summarize choices