PSA_PRACTICE_QNR44. The LCM of two integers a and b is 4,200 and their GCF is 100.If neither a nor b is multiple of the other,find a+b.
Ans: Since, the GCF = 100, let the numbers be 100x and 100y such that x and y do not have any common factors (other than 1).
a + b = 100 (x + y)
LCM = 4200
=> 100 * x * y = 4200
=> xy = 42
(x,y) that satisfy the above equation= (1,42) , (2,21) ,(3,14) , (6,7)
(1,42) set is being rejected based upon the condition “neither a nor b is multiple of the other”.
However, in the rest three case all seem to be satisfying the condition.
Possible sum= 100 (2+21) , 100 (3+14), 100 (6+7)
=2300, 1700, 1300.