Question

Maham has a number of apples. She could share my apples equally among 3, 4, or 5 people. What is the smallest number of apples Maham could have?

Answer 1

Answer:  60

The value 60 is the LCM of 3, 4 and 5.

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Explanation:

LCM = lowest common multiple

To find the LCM, we list out the prime factorization of each number

• 3 = 3*1
• 4 = 2*2
• 5 = 5*1

Ignoring the factors of 1, we have the unique primes of 2, 3, 5. There are 2 copies of '2', one copy of '3', and one copy of '5'. So we multiply this out to get 2*2*3*5 = 4*15 = 60

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If she had 60 apples, and wanted to give them to 3 friends, then each friend gets 60/3 = 20 apples

If instead, she had 4 friends, then each friend gets 60/4 = 15 apples.

Or if she had 5 friends, then each friend gets 60/5 = 12 apples.

For any of those three cases, there are no leftovers or remainders.

Any multiple of 60 will work (eg: 120 or 180), but 60 is the smallest such number that allows her to divide the apples this way without any leftovers.

Answer 2

Answer:

60

Step-by-step explanation:

60 / 3 = 15

60 / 4 = 20

60 / 5 = 12

They all divide evenly.