Question

lesson 44 factors and multiples
find the least common multiple by listing multiples of each number. to list the multiples, write the numbers you say when you skip count by that number. look at each list and circle the numbers shared by both lists. the lowest shared number is the least common multiple.
list the multiples of 3 and 4.
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
4: 4, 8, 12, 16, 20, 24, 28, ...
3 and 4 have 12 and 24 in common.
12 is the least common multiple (lcm).
find the least common multiple of each pair of numbers.

1. 2 and 7 ______
2. 9 and 10 ______
3. 9 and 5 ______
4. 6 and 10 ______
5. 4 and 12 ______
6. 6 and 18 ______
7. 2 and 5 ______
8. 5 and 11 ______
9. 4 and 6 ______

explain why the lcm of two numbers can be the same as one of the numbers. give an example.

Explanation:

Problem 1: Find the least common multiple of 2 and 7

Step 1: List multiples of 2

Multiples of 2: \(2, 4, 6, 8, 10, 12, 14, 16, \dots\)

Step 2: List multiples of 7

Multiples of 7: \(7, 14, 21, 28, \dots\)

Step 3: Identify the least common multiple

The smallest number common to both lists is 14.

Step 1: List multiples of 4

Multiples of 4: \(4, 8, 12, 16, 20, 24, \dots\)

Step 2: List multiples of 10

Multiples of 10: \(10, 20, 30, \dots\)

Step 3: Identify the least common multiple

The smallest number common to both lists is 20.

Step 1: List multiples of 9

Multiples of 9: \(9, 18, 27, 36, 45, \dots\)

Step 2: List multiples of 5

Multiples of 5: \(5, 10, 15, 20, 25, 30, 35, 40, 45, \dots\)

Step 3: Identify the least common multiple

The smallest number common to both lists is 45.

Answer:

14

Problem 2: Find the least common multiple of 4 and 10