Question
Three natural numbers X,Y,Z are
pairwise co-prime and satisfy the following conditions, the least common multiple (LCM) of X and Y is 391, the LCM of Y and Z is 667, If all three numbers are pairwise co-prime natural numbers, find the sum of X+Y+Z.Solution
ATQ, Since, the numbers are co-prime they will have only 1 as the common factor. So, LCM of X and Y = X×Y = 391 LCM of Y and Z = Y×Z = 667 So, X×Y ÷ Y×Z = 391 ÷ 667 X ÷ Z = 17 ÷ 29 Since, it is given that Z is less than 30 and all the numbers are natural numbers. So, X = 17 and Z = 29 Substituting the value of X we get, Y = 23 Therefore, sum of the three numbers = 17 + 23 + 29 = 69
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