hotdogs are sold in packs of 10 and buns are sold in packs of 8, how many packages of each should he buy in order to have the same number of both items

Question

I need an answer to this problem I think the answer is 8*5=40 and 10*4=40

Answer 1

There are two good methods used to find the LCM (Least Common Multiple).

 

Method 1:  List the multiples and choose the lowest common one:

  Multiples of 10:     10    20    30    40    50    60    70    80    90

  Multiples of 8:      8    16   24    32    40    48    56    64    72    80    88

 

Method 2:   List the prime factors and choose the smallest superset:

  Prime factors of 10:    2 * 5

  Prime factors of 8:      2 * 2 * 2

     The smallest superset (contains each of above):    2 * 2 * 2 * 5

 

      2 * 2 * 2 * 5 = 40

 

That means:  Buy 4 packs of hotdogs and 5 packs of buns.  That's 40 of each.