Determine-number-of-possible-pairs-whose-LCM-is-144-in-case-i-when-a-b-amp-b-a-are-considered-same-ii-when-a-b-amp-b-a-are-considered-different-

Question Number 34358 by Rasheed.Sindhi last updated on 05/May/18

Determine number of possible pairs whose

LCM is 144 in case,

(i) when (a, b) & (b, a) are considered same .

(ii) when (a, b) & (b, a) are considered different .

Commented by candre last updated on 05/May/18

144 = 72 \times 2 = 36 \times 2^{2} = 18 \times 2^{3} = 9 \times 2^{4} = 2^{4} \times 3^{2}

S = {x \in N; x ∣ 144}

S = {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144}

∣ S ∣= 5 \times 3 = 15

[\begin{matrix} 1 & 3 & 9 \\ 2 & 6 & 18 \\ 4 & 12 & 36 \\ 8 & 24 & 72 \\ 16 & 48 & 144 \end{matrix}]

Answered by MJS last updated on 05/May/18

(1; 144)

(2; 144)

(3; 144)

(4; 144)

(6; 144)

(8; 144)

(9; 144) (9; 16) (9; 48)

(12; 144)

(16; 144) (16; 18) (16; 36) (16; 72)

(18; 144) (18; 48)

(24; 144)

(36; 144) (36; 48)

(48; 144) (48; 72)

(72; 144)

(144; 144)

(i) 23

(ii) 45

Commented by Rasheed.Sindhi last updated on 05/May/18

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