1

Problem

Find the least common multiple:
45 and 69.

2

Step

The given data

45 and 69

3

Hint

To find the least common multiple (LCM) of 45 and 69, you can use the prime factorization method.

4

Step

Prime factorization of 45:

\$ (3^2) \times (5^1) \$

5

Step

Prime factorization of 69:

\$ (3^2) \times (23^1) \$

6

Step

Next, we identify the highest powers of each prime factor, So the highest power of 3 is:

\$ 3^2 \$

7

Step

The highest power of 5 is:

\$ 5^1 \$

8

Step

The highest power of 23 is:

\$ (23)^1 \$

9

Step

Multiply the highest powers of each prime factor together:

\$ "LCM" = (3^2) \times (5^1) \times (23)^1 \$

10

Step

After simplification:

\$ "LCM" = 9 \times 5 \times 23 \$
LCM = 1035

11

Solution

So the least common multiple is 1035.

12

Sumup

Please summarize steps

Choices

13

Choice-A

This number is not divisible by 45 or 69, as it doesn’t include the proper prime factors

Wrong 1045

14

Choice-B

1035 is correct because it is the smallest number divisible by both 45 and 69

Correct 1035

15

Choice-C

This number is not divisible by 45 and has a remainder of 22. Thus, it cannot be the least common multiple

Wrong 1025

16

Choice-D

This number also lacks the prime factors required to divide both 45 and 69. So, this is wrong

Wrong 1015

17

Step

Option

B

18

Sumup

Please summarize choices