Number System

HCF & LCM

Medium

There are 56 runners and 40 musicians in a school. These students are arranged into groups for a performance, so that each group consists of only runners or musicians, and every group contains an equal number of students. Find the minimum number of groups in which all the students can be accommodated?

✅ Correct Option: 4

To minimise groups, each group must be as large as possible. Since the group size must divide both 56 and 40 evenly, the largest possible group size is $\text{HCF}(56, 40)$ .

$56 = 2 \times 2 \times 2 \times 7$

$40 = 2 \times 2 \times 2 \times 5$

$\text{HCF} = 2 \times 2 \times 2 = 8$

Each group has $8$ students.

Number of groups $= \dfrac{56}{8} + \dfrac{40}{8}$

$= 7 + 5$

$= 12$

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