JAMB 1987 · UME · Q2

Number foundations & fractions

Find the least length of a rod which can be cut into exactly equal strips, each of either 40 cm or 48 cm in length.

Worked solution (try it first)

The length must divide exactly by 40 and by 48, so you want their LCM.
As primes: $40 = 2^3 \times 5$ and $48 = 2^4 \times 3$ .
The LCM is $2^4 \times 3 \times 5 = 240$ .
So the least length is 240 cm, option B.

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