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Question

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 an equal number of biscuits of each brand, then what is the minimum number of packets of each brand he should buy? [4 MARKS]

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Solution

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

For a minimum number of biscuits, first, we find the LCM of 12, 15 and 21.
The prime factors of the following numbers are:
12=2×2×3
15=3×5
21=3×7
The maximum number of times the prime factor 2 occurs is 2.
The maximum number of times the prime factor 3 occurs is 1.
The maximum number of times the prime factor 5 occurs is 1.
The maximum number of times the prime factor 7 occurs is 1.
LCM= 3 × 4 × 5 × 7 = 420
Minimum number of packets of brand A =42012=35
Minimum number of packets of brand B =42015=28
And minimum number of packets of brand C =42021=20

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Month Number of packets sold (in hundreds)
April 73
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June 76
July 86
August 88
September 88
October 89
November 90
December 90
January 105
February 110
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