Question

determine which of the following number pairs have a least common multiple that is greater than 15 and less than 25. select true or false for each number pair.
number pair\ttrue\tfalse
2 and 9\t○\t○
3 and 7\t○\t○
4 and 10\t○\t○
5 and 12\t○\t○

Explanation:

Step1: Analyze 2 and 9

Find LCM of 2 and 9. Prime factors: 2 (2), 9 (3²). LCM = 2×3² = 18. 15 < 18 < 25. So True.

Step2: Analyze 3 and 7

LCM of 3 and 7 is 3×7 = 21. 15 < 21 < 25. So True.

Step3: Analyze 4 and 10

Prime factors: 4 (2²), 10 (2×5). LCM = 2²×5 = 20. 15 < 20 < 25. So True.

Step4: Analyze 5 and 12

LCM of 5 and 12 is 5×12 = 60 (since coprime). 60 > 25. So False.

Answer:

• 2 and 9: True
• 3 and 7: True
• 4 and 10: True
• 5 and 12: False