Question

A child goes to play with some tables in his bag number of pebbles is such that he can arrange them in rows of 18 10 and 15 and form a square in each case how many minimum number of peoples are there in his bag

Answer 1

Given:

The pebbles can be arranged in rows of 18, 15 and 10  to form squares.

To Find:

The minimum number of pebbles needed to be in the bag

Solution:

Find the number of pebbles to form a square with side 18:

Number of pebbles needed = 18 + 18 + 16 + 16

Number of pebbles needed = 68

Find the number of pebbles to form a square with side 15:

Number of pebbles needed = 15 + 15 + 13 + 13

Number of pebbles needed = 56

Find the number of pebbles to form a square with side 10:

Number of pebbles needed = 10 + 10 + 8 + 8

Number of pebbles needed = 36

Find the LCM of 68, 56 and 36:

68 = 2² × 17

56 = 2³ × 7

36 = 2² × 3²

LCM = 2³ x 3² x 7 x  17

LCM = 8568

Answer: The minimum number of pebbles needed is 8568