Stefan purchases materials to make dog collars. stefan purchases 10 buckles in a pack and 12 straps in a pack. stefan doesn't want to have any supplies left over. does stefan need to buy at least 120 of each

No

Step-by-step explanation:

Assuming it take 1 buckle and 1 strap per collar, that means we just need to find the lowest common multiple of these 10-pack buckles and 12-pack straps.

For 10: 0, 10, 20, 30, 40, 50, "60", 70, 80, 90, 100...

For 12: 0, 12, 24, 36, 48, "60", 72, 84, 96, 108, 120...

From this, it is obvious that 60 is the lowest common multiple of these two numbers. Therefore, we know that Stefan can make dog collars without having leftover supplies by using 6 10-pack buckles and 5 12-pack straps.

From this, we know that Stefan does not need to buy 120 of either the buckles or the straps.

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