Mathematics
Three brands A, B and C of biscuits are available in packets of 12, 15 and 21 biscuits respectively. If a shopkeeper wants to buy equal number of biscuits of each brand, what is the minimum number of packets of each brand he should buy?
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Answer
The minimum equal number of biscuits of each brand the shopkeeper should buy is the LCM of 12, 15 and 21.
| 2 | 12, 15, 21 |
|---|---|
| 2 | 6, 15, 21 |
| 3 | 3, 15, 21 |
| 5 | 1, 5, 7 |
| 7 | 1, 1, 7 |
| 1, 1, 1 |
LCM of 12, 15 and 21 = 2 × 2 × 3 × 5 × 7 = 420.
So, the shopkeeper needs 420 biscuits of each brand.
Number of packets of brand A = 420 ÷ 12 = 35.
Number of packets of brand B = 420 ÷ 15 = 28.
Number of packets of brand C = 420 ÷ 21 = 20.
Hence, the shopkeeper should buy 35 packets of brand A, 28 packets of brand B and 20 packets of brand C.
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