Answer:

9 such cuboid candles are needed to make the smallest perfect cube  if candles in the form of cuboids of dimensions 2cm x 3cm x 4cm

Given:

Candles in the form of cuboids of dimensions 2cm x 3cm x 4cm

To Find:

Cuboid candles  needed to make the smallest perfect cube

Solution:

• Volume of cube = (side)³
• Volume of cuboid = length x breadth x Height

Step 1:

Find Volume of cuboid and prime factorize

2 x 3 x 4

= 2 x 3 x 2 x 2

= (2 x 2 x 2) x ( 3)

Step 2:

Need to multiply with 3 x 3  to make perfect cube

= (2 x 2 x 2) x ( 3 x 3 x 3 )

= 2³ x 3³

= 6³

Hence 3 x 3 = 9 cuboids required

9 such cuboid candles are needed to make the smallest perfect cube