Question

- Xoanina oz
EXERS
1. Find the L.C.M. of the following numbers by prime
factorisation method :
(i) 18, 96, 108
(ii) 180, 384, 144
(iii) 20, 25, 30
(iv) 240, 420, 880
(V) 72, 108, 132 (vi) 28, 60, 70,90​

Answer 1

Answer:

(i)
18 = 3 x 3 x 2
96 = 2 x 2 x 2 x 2 x 2 x 3
108 = 3 x 3 x 3 x 2 x 2
L.C.M.(18, 96, 108) = 3³ x 2³ x 2² = 874

(ii)
180 = 5 x 2 x 3 x 2 x 3
384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
144 = 2 x 2 x 3 x 3 x 2 x 2
L.C.M.(180, 384, 144) = 3² x 2³ x 2⁴ x 5 = 5760

(iii)
20 = 5 x 2 x 2
25 = 5 x 5
30 = 3 x 2 x 5
L.C.M.(20, 25, 30) = 5² x 2² x 3 = 300

(iv)
240 = 2 x 2 x 2 x 3 x 5 x 2
420 = 7 x 3 x 2 x 5 x 2
880 = 11 x 2 x 2 x 2 x 5 x 2
L.C.M.(240, 420, 880) = 5 x 2⁴ x 3 x 7 x 11 = 18480

(v)
72 = 2 x 3 x 3 x 2 x 2
108 = 3 x 3 x 3 x 2 x 2
132 = 11 x 3 x 2 x 2
L.C.M.(72, 108, 132) = 3³ x 2³ x 11 = 2376

(vi)
28 = 7 x 2 x 2
60 = 3 x 2 x 5 x 2
70 = 7 x 5 x 2
90 = 3 x 3 x 5 x 2
L.C.M.(28, 60, 70, 90) = 3² x 2² x 5 x 7 = 1260

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