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Ravimade a cuboid of plasticine of dimensions 12cm, 8cm and 3cm. How many minimumnumber of such cuboids will be needed to form a cube?Find the smallest prime number dividing the sum 3+5" |
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Answer» The volume of the cuboid = 12 cm × 8 cm× 3 cm = 288 cu cm The cube is formed by stacking many such cuboids and it will have side lengths which are multiple of 12, 8 and 3. The smallest such cube will have a side length of LCM of 12, 8 and 3. LCM of 12, 8 and 3 - 12 = 2*2*3 8 = 2*2*2 3 = 3 LCM = 2*2*2*3 = 24 The smallest such cube will have side length of 24 and volume (in cu cm) of (24*24*24) cu cm. Number of cuboids of volume (12*8*3) cu cm that will fit into a cube of volume (24*24*24) cu cm. = (24*24*24)/(12*8*3) = 13824/288 = 48 cuboids 3^11 and 5^13 are the product of odd numbers and the number will be oddthe sum of 3^11 and 5^13 is sum of odd numbers and the number will be even the smallest prime number that divides the sum is 2 |
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