Question

multiples - finding the lcm

list the first 5 multiples of the numbers below
example
4: 4, 8, 12, 16, 20

1. 10
2. 3
3. 5
4. 7
5. 12
6. 9
7. 15
8. 20
9. 11
10. 25
11. 8
12. 100
13. 150
14. 135
15. 160
16. 202
17. 250

list the multiples of the numbers below that are between 25 and 45

1. 3
2. 5
3. 4
4. 6
5. 12

list the next 3 multiples of the given numbers that are greater than 100

1. 5
2. 10
3. 8
4. 9
5. 22

list the multiples for each number then circle the lcm of each.

1. 4

10
the lcm is

1. 8

6
the lcm is

1. 11

33
the lcm is

1. 20

15
the lcm is

1. 9

15
the lcm is

1. 35

21
the lcm is

1. 12

20
the lcm is

1. 14

8
the lcm is

1. 12

15
the lcm is

1. 24

18
the lcm is

1. 30

15
45
the lcm is

1. 9

6
12
the lcm is

Explanation:

🆕 New Concept Discovered: Least Common Multiple (LCM)
Finding shared multiples of numbers to locate the smallest one.

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Step 1: List the first 5 multiples (Questions 1–17)

To find the first 5 multiples of a number, multiply the number by 1, 2, 3, 4, and 5.

1. **10**: \(10, 20, 30, 40, 50\)
2. **3**: \(3, 6, 9, 12, 15\)
3. **5**: \(5, 10, 15, 20, 25\)
4. **7**: \(7, 14, 21, 28, 35\)
5. **12**: \(12, 24, 36, 48, 60\)
6. **9**: \(9, 18, 27, 36, 45\)
7. **15**: \(15, 30, 45, 60, 75\)
8. **20**: \(20, 40, 60, 80, 100\)
9. **11**: \(11, 22, 33, 44, 55\)
10. **25**: \(25, 50, 75, 100, 125\)
11. **8**: \(8, 16, 24, 32, 40\)
12. **100**: \(100, 200, 300, 400, 500\)
13. **150**: \(150, 300, 450, 600, 750\)
14. **135**: \(135, 270, 405, 540, 675\)
15. **160**: \(160, 320, 480, 640, 800\)
16. **202**: \(202, 404, 606, 808, 1010\)
17. **250**: \(250, 500, 750, 1000, 1250\)

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Step 2: List multiples between 25 and 45 (Questions 18–22)

Find the multiples of each number that fall strictly between 25 and 45 (inclusive of 25 and 45 if they are multiples).

18. **3**: \(27, 30, 33, 36, 39, 42, 45\)
19. **5**: \(25, 30, 35, 40, 45\)
20. **4**: \(28, 32, 36, 40, 44\)
21. **6**: \(30, 36, 42\)
22. **12**: \(36\)

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Step 3: List the next 3 multiples greater than 100 (Questions 23–27)

Find the smallest multiple of the number that is strictly greater than 100, then list that one and the next two multiples.

23. **5**: The first multiple of 5 greater than 100 is 105.
* Multiples: \(105, 110, 115\)
24. **10**: The first multiple of 10 greater than 100 is 110.
* Multiples: \(110, 120, 130\)
25. **8**: \(8 \times 12 = 96\), \(8 \times 13 = 104\).
* Multiples: \(104, 112, 120\)
26. **9**: \(9 \times 11 = 99\), \(9 \times 12 = 108\).
* Multiples: \(108, 117, 126\)
27. **22**: \(22 \times 4 = 88\), \(22 \times 5 = 110\).
* Multiples: \(110, 132, 154\)

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Step 4: List multiples and find the LCM (Questions 28–31)

List the multiples of each number until you find the first common value (the Least Common Multiple).

28. **4** and **10**:
* Multiples of 4: \(4, 8, 12, 16, 20, 24\)
* Multiples of 10: \(10, 20, 30\)
* **LCM is 20**
29. **8** and **6**:
* Multiples of 8: \(8, 16, 24, 32\)
* Multiples of 6: \(6, 12, 18, 24, 30\)
* **LCM is 24**
30. **11** and **33**:
* Multiples of 11: \(11, 22, 33, 44\)
* Multiples of 33: \(33, 66\)
* **LCM is 33**
31. **20** and **15**:
* Multiples of 20: \(20, 40, 60, 80\)
* Multiples of 15: \(15, 30, 45, 60, 75\)
* **LCM is 60**

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Step 5: Find the LCM (Questions 32–39)

Find the smallest positive integer that is divisible by all the given numbers.

32. **9** and **15**:
* Multiples of 15: 15, 30, 45 (divisible by 9)
* **LCM is 45**
33. **35** and **21**:
* Prime factors: \(35 = 5 \times 7\), \(21 = 3 \times 7\)
* \(\text{LCM} = 3 \times 5 \times 7 = 105\)
* **LCM is 105**
34. **12** and **20**:
* Multiples of 20: 20, 40, 60 (divisible by 12)
* **LCM is 60**
35. **14** and **8**:
* Multiples of 14: 14, 28, 42, 56 (divisible by 8)
* **LCM is 56**
36. **12** and **15**:
* Multiples of 15: 15, 30, 45, 60 (divisible by 12)
* **LCM is 60**
37. **24** and **18**:
* Multiples of 24: 24, 48, 72 (divisible by 18)
* **LCM is 72**
38. **30**, **15**, and **45**:
* Multiples of the largest number (45): 45, 90 (divisible by both 30 and 15)
* **LCM is 90**
39. **9**, **6**, and **12**:
* Multiples of the largest number (12): 12, 24, 36 (divisible by both 9 and 6)
* **LCM is 36**

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Answer:

List the first 5 multiples:

1. 10: 10, 20, 30, 40, 50
2. 3: 3, 6, 9, 12, 15
3. 5: 5, 10, 15, 20, 25
4. 7: 7, 14, 21, 28, 35
5. 12: 12, 24, 36, 48, 60
6. 9: 9, 18, 27, 36, 45
7. 15: 15, 30, 45, 60, 75
8. 20: 20, 40, 60, 80, 100
9. 11: 11, 22, 33, 44, 55
10. 25: 25, 50, 75, 100, 125
11. 8: 8, 16, 24, 32, 40
12. 100: 100, 200, 300, 400, 500
13. 150: 150, 300, 450, 600, 750
14. 135: 135, 270, 405, 540, 675
15. 160: 160, 320, 480, 640, 800
16. 202: 202, 404, 606, 808, 1010
17. 250: 250, 500, 750, 1000, 1250

Multiples between 25 and 45:

1. 3: 27, 30, 33, 36, 39, 42, 45
2. 5: 25, 30, 35, 40, 45
3. 4: 28, 32, 36, 40, 44
4. 6: 30, 36, 42
5. 12: 36

Next 3 multiples greater than 100:

1. 5: 105, 110, 115
2. 10: 110, 120, 130
3. 8: 104, 112, 120
4. 9: 108, 117, 126
5. 22: 110, 132, 154

List multiples and find LCM:

1. 4: 4, 8, 12, 16, 20; 10: 10, 20; LCM is 20
2. 8: 8, 16, 24; 6: 6, 12, 18, 24; LCM is 24
3. 11: 11, 22, 33; 33: 33; LCM is 33
4. 20: 20, 40, 60; 15: 15, 30, 45, 60; LCM is 60

Find the LCM:

1. 9, 15: LCM is 45
2. 35, 21: LCM is 105
3. 12, 20: LCM is 60
4. 14, 8: LCM is 56
5. 12, 15: LCM is 60
6. 24, 18: LCM is 72
7. 30, 15, 45: LCM is 90
8. 9, 6, 12: LCM is 36