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# An man inspects every 36th egg for cracks and every 48th egg for weight. What is the fist egg he checks for both?

A man inspects every 36th egg for cracks and every 48th egg for weight. What is the first egg he checks for both?

### 3 Answers by Expert Tutors

David S. | Wise Math TutorWise Math Tutor
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1
Here you go Brian...

Since he checks every 36th egg for cracks and every 48th egg for weight let x = a multiple of 36 and let y = a multiple of 48.  for the two to happen together we know that 36x = 48y.

Then rearranging we know that x/y = 48/36.  Reducing the ratio of x/y = 4/3

So (36)(4) = (48)(3) = 144.  So the 1st egg checked for both would be egg 144.
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
1
And that will be the number you will can divide by 36 and 48. It calls Least Common Multiple (LCM).
Let's use prime factorization:

36 = 2 × 2 ×             3 × 3
48 = 2 × 2 × 2 × 2 × 3
↓     ↓     ↓    ↓    ↓     ↓
LCM = 2 × 2 × 2 × 2 × 3 × 3

LCM (36, 48) = 144

144th egg will be inspect for cracks and weight.