Question

Tom and Larry are food inspectors at a cookie making company. Tom tests every 8th batch of dough for fat percentage. Larry tests every 28th batch of dough for carbohydrate percentage. If they both start working at the same time, which batch will be the first that they both test?

Answer 1

Explanation:

8=2x2x2

28=2x2x7

lcm of 8,28= 56

Answer 2

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Answer:

56th batch

Explanation:

The least common multiple of 8 and 28 is 8·7 = 56. Tom and Larry will both test the 56th batch.

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There are a couple of ways to find the least common multiple (LCM) of a pair of numbers.

1. Factor them and use the highest power of the unique factors.

8 = 2³

28 = 2²×7

Unique factors are 2 and 7. Their highest powers are 3 and 1, so the LCM is ...

(2³)(7) = 56

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2. Divide the product by the greatest common divisor (GCD). Here, both numbers are divisible by 4:

8 = 4·2

28 = 4·7

So, the LCM is 8×28/4 = 56.