Question

1. match each pair of numbers with the pair of numbers that has the same lcm.

same lcm as 6, 8
same lcm as 4, 10
same lcm as 5, 8
same lcm as 8, 20
8, 10
4, 5
30 3-2 find greatest common factor and least common multiple

1. which expression is equivalent to 42 + 70?

ⓐ 6(7 + 10)
ⓑ 7(7 + 10)
ⓒ 14(3 + 5)
ⓓ 21(2 + 3)

Explanation:

Step1: Find LCM of 6,8

Prime factors: \(6 = 2\times3\), \(8 = 2^3\). LCM is \(2^3\times3 = 24\). Check 8,10: \(8 = 2^3\), \(10 = 2\times5\), LCM \(2^3\times5 = 40\) (no). 4,5: \(4 = 2^2\), \(5\) prime, LCM \(20\) (no). Wait, maybe 8,10? No, recheck. Wait, 6,8 LCM 24. Now 8,10 LCM 40, 4,5 LCM 20. Wait, maybe first row: "Same LCM as 6,8" – find pair with LCM 24. 8,10 LCM 40, 4,5 LCM 20. Wait, maybe I made a mistake. Wait, 6,8: LCM 24. Now check 8,10: LCM 40, 4,5: LCM 20. Wait, maybe the pairs are 8,10? No. Wait, maybe the second row: "Same LCM as 4,10". 4,10: \(4 = 2^2\), \(10 = 2\times5\), LCM \(2^2\times5 = 20\). So pair with LCM 20: 8,20? \(8 = 2^3\), \(20 = 2^2\times5\), LCM \(2^3\times5 = 40\) (no). 4,5: LCM 20 (yes). So 4,5 has LCM 20, same as 4,10? Wait 4,10 LCM 20, 4,5 LCM 20. Yes. So "Same LCM as 4,10" matches 4,5.

Step2: LCM of 5,8: \(5\) prime, \(8 = 2^3\), LCM \(40\). 8,10: \(8 = 2^3\), \(10 = 2\times5\), LCM \(40\). So "Same LCM as 5,8" matches 8,10.

Step3: LCM of 8,20: \(8 = 2^3\), \(20 = 2^2\times5\), LCM \(40\). Wait no, 8,20 LCM: \(2^3\times5 = 40\). 5,8 LCM 40, 8,10 LCM 40. Wait, maybe "Same LCM as 8,20" – 8,20 LCM 40. 8,10 LCM 40, 5,8 LCM 40. So "Same LCM as 8,20" matches 5,8? Wait, no, let's re-express:

• "Same LCM as 6,8" (LCM 24): Which pair? Wait, maybe 8,10? No, LCM 40. Wait, maybe the table is:

First column (top) pairs: 8,10 and 4,5.

Rows:

1. Same LCM as 6,8 (LCM 24) – no pair? Wait, maybe the problem is to match each pair (8,10; 4,5) with the "Same LCM as..." rows.

Wait, let's list all LCMs:

• 6,8: LCM 24
• 4,10: LCM 20
• 5,8: LCM 40
• 8,20: LCM 40

Pairs to match: 8,10 (LCM 40) and 4,5 (LCM 20).

So:

• "Same LCM as 6,8" (24): no match (8,10 LCM 40, 4,5 LCM 20) – maybe error, but proceed.

• "Same LCM as 4,10" (20): matches 4,5 (LCM 20)
• "Same LCM as 5,8" (40): matches 8,10 (LCM 40)
• "Same LCM as 8,20" (40): matches 8,10 (LCM 40) or 5,8 (LCM 40). But 8,10 and 5,8 both have LCM 40.

Assuming the table is:

Row 1: Same LCM as 6,8 – maybe 8,10? No, LCM 40. Wait, maybe I misread. Let's do each:

1. Same LCM as 6,8: LCM 24. Pairs: 8,10 (LCM 40), 4,5 (LCM 20) – no. Wait, maybe the first column is 8,10 and 4,5, and the rows are the "Same LCM as..."

Wait, the first column (top) has two pairs: 8,10 (first row) and 4,5 (second row).

Rows (from top):

1. Same LCM as 6,8
2. Same LCM as 4,10
3. Same LCM as 5,8
4. Same LCM as 8,20

So:

• Row 2 (Same LCM as 4,10: LCM 20) matches 4,5 (LCM 20) – so 4,5 in row 2.

• Row 3 (Same LCM as 5,8: LCM 40) matches 8,10 (LCM 40) – so 8,10 in row 3.

• Row 4 (Same LCM as 8,20: LCM 40) also matches 8,10 (LCM 40) or 5,8 (but 5,8 is not a pair here, pairs are 8,10 and 4,5). So 8,10 in row 4.

• Row 1 (Same LCM as 6,8: LCM 24) – no match, but maybe I made a mistake. Wait, 6,8 LCM 24. Is there a pair? 8,10 LCM 40, 4,5 LCM 20. No. Maybe the problem has a typo, but proceed with the matches we can do.

Answer:

• Same LCM as 4,10: 4,5
• Same LCM as 5,8: 8,10
• Same LCM as 8,20: 8,10

(Note: The first row "Same LCM as 6,8" may have no match with given pairs, but based on LCM calculations, the above matches are correct for the other rows.)