Question

pencils are sold in boxes of 10 erasers are sold in boxes of 14. a teacher wants to buy the same number of pencils and erasers. work out the smallest number of boxes of each item she should buy

Answer 1

Answer:

pencil have smallest no of box

Answer 2

The teacher should buy 7 boxes of pencils and 5 boxes of erasers

Solution:

Pencils are sold in boxes of 10 erasers are sold in boxes of 14

Teacher wants to buy the same number of pencils and erasers

Find the LCM of 10 and 14

List all prime factors for each number.

Prime Factorization of 10 is:  2 x 5

Prime Factorization of 14 is:  2 x 7  

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 5 x 7 = 70

Work out the smallest number of boxes of each item she should buy :

$boxes\ of\ pencil = \frac{70}{10} = 7 \\\\boxes\ of\ erasers = \frac{70}{14} = 5$

Thus the teacher should buy 7 boxes of pencils and 5 boxes of erasers

Learn more:

Colour pencils are sold in boxes of 10 each.a shopkeeper has 90 colour pencils.how many boxes can he make

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Colour pencils are sold in boxes of 10 each.a shop keeper has 90 colour pencils.how many boxes can he make?

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