John took his pennies out of his piggy bank and discovered that he could put his pennies in equal piles of three, four, five, six, seven or eight. What is the least number of pennies that he could have had?

Question

Mathematics

Ruby

7 February, 06:36

John took his pennies out of his piggy bank and discovered that he could put his pennies in equal piles of three, four, five, six, seven or eight. What is the least number of pennies that he could have had?

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Answers (2)

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Barbara Frey · Answer 1

Least number of pennies is 840

Step-by-step explanation:

To get the least number of pennies, we need to figure out the LCM of 3, 4, 5, 6, 7, & 8.

We do prime factorization of each number and take each unique digit the most number of times it occurs in any one of them.

3 is 3

4 is 2*2

5 is 5

6 is 3*2

7 is 7

8 is 2*2*2

There are 2s, 3s, 5s, and 7s. Two occurs three times (highest) in 8, so we take 2 three times, 3,4,5,&7 all occur highest 1 time. So we take them one.

So LCM = 2*2*2*3*5*7 = 840

Lucian Benitez · Answer 2

Lucian Benitez 7 February, 10:35

0

The answer is 840 I think