1

Problem

Find the least common multiple for the following numbers:
6 and 15.

2

Step

The given numbers are

6 and 15

3

Hint

To find the least common multiple (LCM) of 6 and 15, you can use the prime factorization method.

4

Step

Prime factorization of 6:

\$ (2)^1 \times (3)^1\$

5

Step

Prime factorization of 15:

\$ (3)^1 \times (5)^1 \$

6

Step

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

\$ 2^1 \$

7

Step

The highest power of 3 is:

\$ 3^1 \$

8

Step

The highest power of 5 is:

\$ 5^1 \$

9

Step

Multiply the highest powers of each prime factor together:

\$ "LCM" = (2)^1 \times (3)^1 \times (5)^1\$

10

Step

After multiplication:

\$ "LCM" = 2 \times 3 \times 5 \$
LCM = 30

11

Solution

So, therefore the least common multiple is 30.

12

Sumup

Please summarize steps

Choices

13

Choice-A

This is correct because it is the least common multiple of 6 and 15

Correct 30

14

Choice-B

This is the LCM of 4 and 8, not 6 and 15. 16 is not divisible by both 6 and 15.

Wrong 16

15

Choice-C

This option is wrong because the LCM of 16 and 32, not 6 and 15. 32 is not divisible by both 6 and 15

Wrong 25

16

Choice-D

This is incorrect because 32 is not the smallest number that can be divided evenly by both 6 and 15

Wrong 32

17

Step

Option

A

18

Sumup

Please summarize choices