TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5

Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.5

Question 1.
Find the LCM of the following numbers by prime factorisation method.
(i) 12 and 15
Answer:
The given numbers are 12 and 15.
Let us e×press each number as a product of prime factors.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 1
The common factor of both = 3
Take the extra factors of both 12 and 15, (i.e.,) 2, 2 and 5
∴ LCM = 2 × 2 × 5 × 3 = 60

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5

(ii) 15 and 25
Answer:
The given numbers are 15 and 25.
Let us express each number as the product of prime factors.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 5
The common factor of both = 5
The extra factors of both = 3 and 5
∴ LCM = 3 × 5 × 5 = 75.

(iii) 14 and 21
Answer:
The given numbers are 14 and 21.
Let us express each number as the product of prime factors.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 2
The common factor of both = 7
The extra factors of both = 2 and 3
∴ LCM = 2 × 3 × 7 = 42

(iv) 18 and 27
Answer:
The given numbers are 18 and 27
Let us express each number as the product of prime factors.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 3
The common factor of both = 3 × 3
The extra factors of both = 2 and 3
∴ LCM = 3 × 3 × 2 × 3 = 54

(v) 48, 56 and 72
Answer:
The given numbers are 48, 56 and 72.
Let us express each number as the product of prime factors.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 4
The common factor of the three numbers = 2 × 2 × 2 × 3
The extra factors of the three numbers = 2 × 3 × 7
∴ LCM = 2 × 2 × 2 × 3 × 2 × 3 × 7 = 1008

(vi) 26, 14 and 91
Answer:
The given numbers are 26, 14 and 91
Let us express each number as the product of prime factors
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 6
The common factors of the three numbers = 2 × 13 × 7
There are no extra factors of all the numbers.
∴ LCM = 2 × 13 × 7 = 182

Question 2.
Find the LCM of the following numbers by division method,
(i) 84, 112, 196
Answer:
The given numbers are 84, 112 and 196.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 7
∴ LCM = 2 × 2 × 7 × 3 × 4 × 7 = 2352

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5

(ii) 102, 119, 153
Answer:
The given numbers are 102, 119 and 153.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 8
∴ LCM = 17 × 3 × 2 × 7 × 3 = 2142

(iii) 45, 99, 132, 165
Answer:
The given numbers are 45, 99, 132 and 165.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 9
∴ LCM = 3 × 11 × 5 × 3 × 4 = 1980

Question 3.
Find the smelliest number which when added to 5 is exactly divisible by 12, 14 and 18.
Answer:
Let us find the LCM of 12, 14 and 18.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 10
∴ LCM = 2 × 3 × 2 × 7 × 3 = 252
∴ The required smallest number = 252 – 5 = 247

Question 4.
Find the greatest 3 digit number which when divided by 75,45 and 60 leaves:
(i) no remainder
(ii) the remainder 4 in each case.
Answer:
(i) The given numbers are 75, 45 and 60.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5 11
∴ LCM = 5 × 3 × 5 × 3 × 4 = 900
∴The required number with no remainder = 900

(ii) The required number with
remainder 4 in each case = 900 + 4 = 904

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.5

Question 5.
Prasad and Raju met in the market on 1st of this month. Prasad goes to the market every 3rd day and Raju goes every 4th day. On what day of the month will they meet again ?
Answer:
The day on which Prasad and Raju met in the market is 1st of this month.
Prasad goes to the market every 3rd day.
Raju goes to the market every 4th day.
To find the day on which they meet again, we have to find the LCM of 3 and 4.
LCM of 3 and 4 = 3 × 4 = 12
So, Raju and Prasad meet again after 12 days.
(i.e.,) They meet again on 13th day of this month.

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