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If the LCM of two numbers is equal to the product of the two numbers, what must be true about their common factor?

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2 Answers

Since LCM(A,B) = (A*B)/(GCF(A,B)), then GCF(A,B) = (A*B)/LCM(A,B).
 
If the LCM(A,B) = A*B, then GCF(A,B) = (A*B)/LCM(A,B) = (A*B)/(A*B) = 1.
 2 numbers don't have any common factors.
 
      LCM (A, B)  = AB/ Gcf
 
       Example :  A = 24 = 23 * 3
                       B= 36 =  22 * 32
 
                        GCF = 22 * 3 = 12  / product of common factors with lowest exponent.
 
                         LCM = 23 * 32 = 8(9) = 72  / Equals product of common factors with highest exponent .
 
                           LCM = (36) (24)  = 72
                                        12
         This means that to find the lowest number which 2 numbers can be divided into that, the greatest
              common factor is multiplied only once
               Like the above example:
 
                  24 = 23 * 3
                 36 = 22 * 32  
 
                  between 8 and 4 , 8 =2is divisible both to 8 and 4
                  Between 3 and 9,  9 = 32 is divisible to both 9 and 3
 
                   Their product  8 * 9 = 72 is divisible to both 24, 36.
                    Which is  
                                  (24) (36) = 72
                                      12 (GCF)
 
              If 2 numbers like 22, 45
 
                                        22 = 2 *11
                                        45 = 32 * 5
 
                      Don't have any common factor, therefore , LCM = 22* 45 = 990