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

Question

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

Answer 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

144^th egg will be inspect for cracks and weight.

Answer 2

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.

Answer 3

Hey Brian -- since they're eggs, think "dozens" ... crack-scan 3doz, 6doz, 9doz, 12doz

... wt-scan 4doz, 8doz, 12doz ==> intersect at 12 doz or 144th egg ... Regards, sir :)