
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 = 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.
—
✅ Step 1: Prime factorizations
21 = 3 × 7
42 = 2 × 3 × 7
56 = 2³ × 7
Common factor = 7
✅ HCF = 7
—
✅ 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
—
✅ Final Answer: Minimum number of rows = 17