Smallest number multiplied to form a Perfect Cube

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Smallest number multiplied to form a Perfect Cube Let’s do this by examples Question Finds the smallest number multiplied to 1125 to get a perfect cube We see that, 1125 = 3 × 3 × 5 × 5 × 5 Since 3 does not occur triplets, we multiply by 3 to make a triplet So, our number becomes 1125 × 3 = 3 × 3 × 5 × 5 × 5 × 3 = 3 × 3 × 3 × 5 × 5 × 5 Now, it becomes a perfect cube. So, we multiply 1125 by 3 to make it a perfect cube Question Finds the smallest number multiplied to 5324 to get a perfect cube. We see that, 5324 = 2 × 2 × 11 × 11 × 11 Here, 2 does not occur in triplets So, we multiply by 2 to make triplet So, our number becomes 5324 × 2 = 2 × 2 × 11 × 11 × 11 × 2 = 2 × 2 × 2 × 11 × 11 × 11 Now, it becomes a perfect cube. So, we multiply 5324 by 2 to make it a perfect cube Question Finds the smallest number multiplied to 968 to get a perfect cube. We see that, 968 = 2 × 2 × 2 × 11 × 11 Here, 11 does not occur in triplets So, we multiply by 11 to make triplet So, our number becomes 968 × 11 = 2 × 2 × 2 × 11 × 11 × 11 Now, it becomes a perfect cube. So, we multiply 968 by 11 to make it a perfect cube Question Finds the smallest number divided to 400 to get a perfect cube. We see that, 400 = 2 × 2 × 2 × 2 × 5 × 5 Here, 2 & 5 does not occur in triplets So, we multiply by 2 × 2 × 5 to make triplet So, our number becomes 400 × 2 × 2 × 5 = 2 × 2 × 2 × 2 × 5 × 5 × 2 × 2 × 5 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 Now, it becomes a perfect cube. So, we multiply 400 by 2 × 2 × 5 i.e. 20 to make it a perfect cube