If three numbers x - y - z -2-3- 7-6- 8-9 and 108 L - C - M - - H - C - F - p - q where p - q are coprime to each other- then the total number ofposiible pairs of p - q A- 4B- 2C- 8D- 6

The correct option is A 4L.C.M. of nbsp;23,76,89 is 563 H.C.F. of nbsp;23,76,89 is 118 108(563×118)=112 Now, factors of 112 are {1,2,4,7,8,14,16,28,56,112} ...

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Byju's Answer

Standard XII

Mathematics

LaGrange's Mean Value theorem

If three numb...

Question

If three numbers $(x, y, z) = (\frac{2}{3}, \frac{7}{6}, \frac{8}{9})$ and $108 (L.C.M. \times H.C.F.) = p \times q$ where $p, q$ are coprime to each other, then the total number of posiible pairs of $(p, q)$ is

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Solution

The correct option is A $4$
L.C.M. of $\frac{2}{3}, \frac{7}{6}, \frac{8}{9}$ is $\frac{56}{3}$
H.C.F. of $\frac{2}{3}, \frac{7}{6}, \frac{8}{9}$ is $\frac{1}{18}$
$108 (\frac{56}{3} \times \frac{1}{18}) = 112$
Now, factors of $112$ are ${1, 2, 4, 7, 8, 14, 16, 28, 56, 112}$
Possible coprime pairs are $(1, 112), (7, 16), (16, 7), (112, 1)$

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If three numbers (x,y,z)=(23,76,89) and 108(L.C.M.×H.C.F.)=p×q where p,q are coprime to each other, then the total number of posiible pairs of (p,q) is

The correct option is A 4L.C.M. of 23,76,89 is 563 H.C.F. of 23,76,89 is 118 108(563×118)=112 Now, factors of 112 are {1,2,4,7,8,14,16,28,56,112} Possible coprime pairs are (1,112),(7,16),(16,7),(112,1)

If three numbers $(x, y, z) = (\frac{2}{3}, \frac{7}{6}, \frac{8}{9})$ and $108 (L.C.M. \times H.C.F.) = p \times q$ where $p, q$ are coprime to each other, then the total number of posiible pairs of $(p, q)$ is