Page 138 - Ganit Kaushal

(b) Factors of 5 are 1 and 5;

Factors of 15 are 1, 3, 5, and 15.
Factors of 25 are 1, 5 and 25.
\ Common factors of 5, 15 and 25 are 1, 5.
Ex 3. Find the first three common multiples of: (a) 6 and 8, (b) 12 and 18.
Sol. (a) Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, ....

Therefore, the first three common multiples of 6 and 8 are 24, 48, and 72.
(b) Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, ...
Therefore, the first three common multiples of 12 and 18 are 36, 72, and 108.
Ex 4. Write all the numbers less than 100 which are common multiples of 3 and 4.
Sol. Multiples of 3 less than 100 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, and so on.
Multiples of 4 less than 100 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, and so on.

Common multiples of 3 and 4 are 12, 24, 36, and so on i.e., multiples of 12.
\ Common multiples of 3 and 4 that are less than 100 are 12, 24, 36, 48, 60, 72, 84, 96.
Ex 5. Find any three numbers that are multiples of 25 but not multiples of 50. (NCERT)
Sol. Multiples of 25 are 25, 50, 75, 100, 125, …; Multiples of 50 are 50, 100, 150, …
\ Three numbers that are multiples of 25 but not multiples of 50 are 25, 75, 125.
Ex 6. Aashu and his friends play the ‘Dahi-Vada’ game with two different numbers, which are both smaller
than 10. The first time anybody says ‘Dahi-Vada’ is after the number 50. What could the two numbers
be which are assigned ‘Dahi’ and ‘Vada’? (NCERT)
Sol. The two numbers, which are assigned ‘Dahi’ and ‘Vada’, could be 7 and 8, or 7 and 9, or 8 and 9,
respectively. If 7 and 9 are taken as ‘Dahi’ and ‘Vada’ respectively, then the first time anybody says
Dahi-Vada is for the number 63 which is greater than 50 (9 × 7  9 and 7 are co-prime).
Similarly, we do this for other numbers.
Ex 7. At what number is ‘Dahi-Vada’ said for the 10th time? (NCERT)
Sol. The first number for which the player should say ‘Dahi-Vada’ is 15, which is a multiple of 3 and 5.

So, 15 × 1 = 15; 15 × 2 = 30; 15 × 3 = 45, ..., 15 × 10 = 150.
\ 150 is the number for which ‘Dahi-Vada’ is said for the 10th time.
Ex 8. If the game is played for the numbers from 1 till 90, find out:
(a) How many times would the children say ‘Dahi’, including the times they say ‘Dahi-Vada’?
(b) How many times would the children say ‘Vada’, including the times they say ‘Dahi-Vada’?
(c) How many times would the children say ‘Dahi-Vada’? (NCERT)
Sol. (a) Multiples of 3 from 1 till 90 = 3, 6, 9, 12, …, 90; (90 ÷ 3) = 30 times.

(b) Multiples of 5 from 1 till 90 = 5, 10, 15, …, 90; (90 ÷ 5) = 18 times.
(c) Common multiples of 3 & 5 from 1 till 90 = 15, 30, 45, 60, 75, 90; (90 ÷ 15) = 6 times.
Ex 9. What if the game was played till 900? How would your answers change? (NCERT)
Sol. All answers of example 8 will be multiplied by 10. So, the answers are 300 times, 180 times, and 60
times.

136 Mathematics-6