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I think it's easier to find the possible numbers that have a product of 72 first. These would be

1 and 72; 2 and 36; 3 and 24; 4 and 18; 6 and 12; 8 and 9

Now let's find the LCM's of each pair

1 and 72= 72; 2 and 36=36; 3 and 24= 24; 4 and 18=36; 6 and 12=12; 8 and 9=72

Actually, two pairs of numbers have both an LCM of 36 and a product of 72:

2 and 36; 4 and 18

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Q: What pair of numbers has an LCM of 36 and a product of 72?

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