Question

Find the smallest number by which the number 72 must be multiplied to obtain a perfect cube (a) 2 (b) 3 (c) 4 (d) 6.​

Answer 1

Step-by-step explanation:

LCM = 2 × 2 × 2 × 3 × 3

in the above factorisation , 3 does not appear in the group of three ( triplets )

therefore, 72 is not a perfect cube.

to make it a perfect cube we need one more 3.

thus, 72 × 3 = 216 = 2×2×2×3×3×3 = 2³ × 3³.

Which is a perfect cube.

hence, the smallest number by which 72 should be multiplied to make a perfect cube is 3.

so, option A is correct.

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