1

Problem

Find the least common multiple:
41 and 55.

2

Step

The given data

41 and 55

3

Hint

To find the least common multiple (LCM) of 41 and 55, you can use the prime factorization method.

4

Step

Prime factorization of 41:

\$ (41)^1 \$

5

Step

Prime factorization of 55:

\$ 5^1 \times (11)^1 \$

6

Step

Next, we identify the highest powers of each prime factor. So the highest power of 41 is:

\$ 41^1 \$

7

Step

The highest power of 5 is:

\$ 5^1 \$

8

Step

The highest power of 11 is:

\$ (11)^1 \$

9

Step

Multiply the highest powers of each prime factor together:

\$ LCM = (41)^1 \times (5)^1 \times (11)^1\$

10

Step

Make it simplify:

\$ "LCM" = 41 \times 5 \times 11 \$
LCM = 2255

11

Solution

So, the least common multiple is 2255.

12

Sumup

Please summarize steps

Choices

13

Choice-A

2245 cannot be the LCM because it is not divisible by 41 (check \$(2245)/(41) = 54.756\$, not an integer)

Wrong 2245

14

Choice-B

This is incorrect because it isn’t divisible by both 41 and 55

Wrong 2265

15

Choice-C

2205 cannot be the LCM because it is not divisible by 41 (check \$(2205)/(41) = 53.78\$, not an integer)

Wrong 2205

16

Choice-D

This is the correct answer because it is the least common multiple of 41 and 55

Correct 2255

17

Step

Option

D

18

Sumup

Please summarize choices