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Find the LCM of each of the following group of numbers by prime factorisation.(c) 300, 400, 700 |
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Answer» L.C.M. of 18, 24 and 96 (i) By prime factors Prime factors of 18 = 2 x 3 x 3 Prime factors of 24 = 2 x 2 x 2 x 3 Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3 L.C.M. = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288 By common DIVISION method L.C.M. of 18, 24 and 96 = 2 x 2 x 2 x 3 x 3 x 4 = 288 (ii) 100, 150 and 200 Factor of 100 = 2 × 2 × 5 × 5 = 22 × 52 Factor of 150 = 2 × 3 × 5 × 5 = 21 × 31 × 52 Factor of 200 = 2 × 2 × 2 × 5 × 5 = 23 × 52 ∴ L.C.M. OF 100, 150 and 200 = 23 × 31 × 52 = 600 ∴ L.C.M. OF 100, (iii) 14, 21, 98 Factor of 14 = 2 × 7 = 21 × 71 Factor of 21 = 3 × 7 = 31 × 71 Factor of 98 = 2 × 7 × 7 = 21 × 72 ∴ L.C.M. of 14, 21 and 98 = 21 × 31 × 72 = 294 (v) 34, 85 and 51 Factor of 34 = 2 ×17 = 21 × 171 Factor of 85 = 5 × 17 = 51 × 171 Factor of 51 = 3 × 17 = 31 × 171 ∴ L.C.M. of 34, 85 and 51 = 21 × 51 × 31 × 17 = 510 ∴ L.C.M. OF 34, 85 and 51 = 2 × 17 × 5 × 3 = 510 |
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