Page 49 - Maths Class 06

EX AM PLE 2. The floor of a hall is 15.5 m and 10.5 m. Square-shaped tiles are to be fixed on it. Find the
larg est size of tile and also find the num ber of tiles re quired to cover the floor of the hall
com pletely.

SO LU TION : The larg est size of tile will be the HCF of 15.5 m and 10.5 m.
We know that,
15.5 m = 1550 cm 2 1550 2 1050

and 10.5 m = 1050 cm 5 775 3 525
We shall find the HCF of 1550 and 1050. 5 155 5 175

Now, 1550 = 2 5 5 31´ ´ ´
31 31 5 35
b
1 7 7
and 1050 = 2 3 5 5 7´ ´ ´ ´
1
\ The HCF of 1550 and 1050 is 2 5 5´ ´ , i e. . 50.
Thus, the largest size of the tile is 50 cm.
)
Now, Area of the floor of the hall =(1500 1050 sq. cm
´
)
Area of one tile =(50 50 sq. cm
´
1550 ´1050
\ Number of tiles required = = 31 21 651
´
=
50 ´50
Also, recall that LCM of two or more numbers is the smallest number which is exactly
divisible by each of the given numbers.
EX AM PLE 3. Find the least (small est) num ber which is ex actly di vis i ble by 8, 10 and 12.
SO LU TION : The re quired num ber is LCM of 8, 10 and 12.

Now, 8 = 2 2 2´ ´
10 = 2 5´
12 = 2 2 3´ ´

\ LCM = ´ ´ ´ ´ =2 2 2 3 5 120
Thus, the required number is 120.

EX AM PLE 4. Find the least 3-digit num ber which when di vided by 18, 24 and 32 leaves a re main der 7 in
each case.
SO LU TION : The re quired num ber is 7 added to the LCM of 18, 24 and 32.
Now, 18 = 2 3 3´ ´

24 = 2 2 2 3´ ´ ´
32 = 2 2 2 2 2´ ´ ´ ´
\ LCM = ´ ´ ´ ´ ´ ´ =2 2 2 2 2 3 3 288

Hence, the required number is 288 7+ = 295.
EX AM PLE 5. In a morn ing walk, three friends step off to gether. Their steps mea sure 80 cm, 85 cm and
90 cm re spec tively. What is the min i mum (least) dis tance each should cover so that all can
cover the same dis tance in com plete steps?

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