Find Interview Questions for CAST Software India

We are given:

• Seeta made necklaces of either 16, 20, or 36 beads.

• No bead was left over in any case.

• We are to find the least number of beads she could have had.

🧠 This is a classic LCM problem.

We are to find the Least Common Multiple (LCM) of 16, 20, and 36.

🔹 Step 1: Prime factorization

• 16 = 2⁴

• 20 = 2² × 5

• 36 = 2² × 3²

Now take the highest powers of all primes:

• 2⁴, 3², 5

LCM=24×32×5=16×9×5=144×5=720\text{LCM} = 2⁴ × 3² × 5 = 16 × 9 × 5 = 144 × 5 = 720LCM=24×32×5=16×9×5=144×5=720

✅ Final Answer:
Seeta had at least 720 beads.

• 21 mango trees

• 42 apple trees

• 56 orange trees

We want to plant them in rows such that:

• Each row contains only one type of tree

• Each row has the same number of trees

• The number of rows is minimized

🧠 This is a Highest Common Factor (HCF) problem.

We need to find the HCF of 21, 42, and 56.

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✅ Step 1: Prime factorizations

• 21 = 3 × 7

• 42 = 2 × 3 × 7

• 56 = 2³ × 7

Common factor = 7

✅ HCF = 7

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✅ Step 2: Find number of rows for each type:

• Mango: 21 ÷ 7 = 3 rows

• Apple: 42 ÷ 7 = 6 rows

• Orange: 56 ÷ 7 = 8 rows

✅ Total rows = 3 + 6 + 8 = 17 rows

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✅ Final Answer: Minimum number of rows = 17