In a morning walk, Nirmaljeet, Puneet and Raju step off together, their steps measuring 240cm,
90cm and 120cm respectively. They want to go for a juice shop for a health issue, which is situated
near by them.
(a) Find the minimum distance of shop from where they start to walk together, so that one can cover
the distance in complete steps?
(i) 720 cm (ii) 700cm (iii) 620cm (iv) 740 m
(b) Find the number of common steps cover by all of them to reach the juice shop.
(i) 20 (ii) 30 (iii) 35 (iv) 40
(c) If a and b are two number, then find the relation between LCM and HCF.
(i)
= (, ) (, ) (ii) a × = (, ) = × (, )
(iii) a × LCM (a,b) = b × HCF (a,b) (iv) None of the above
(d) A largest positive integer that divides given two positive integers is called.
(i) HCF (ii) LCM (iii) flower (iv) None of the above
Answers
Answer:
GIVEN:-
Measurements of steps:-
Nirmaljeet - 240cm
Puneet - 90cm
Raju - 120cm
SOLUTION
(a) Minimum distance
In this case we have to find the LCM (240,90,120)
240 = 2 x 2 x 2 x 3 x 2 x5
120 = 2 x 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5
LCM = 720
(i) 720
(b) Common distance
In this case we have to find the HCF (240,90,120)
240 = 2 x 2 x 2 x 3 x 2 x5
120 = 2 x 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
HCF = 2 x 3 x 5
HCF = 30
(ii) 30
(c) Relation
Now we have a = 720 and b = 30
LCM (a,b) x HCF (a,b) = a x b
(d) Largest positive integer that divides given two positive integers
HCF ( Highest Common Factor )
Answer:
(a) The minimum distance of shop from where they start to walk together, so that one can cover the distance in complete steps is option(1) 720cm.
(b) The number of common steps covered by all of them to reach the juice shop is option(2) 30.
(c)If a and b are two numbers, then the relation between LCM and HCF is LCM(a, b)×HCF(a, b) = a × b.
(d)A largest positive integer that divides given two positive integers is called option(1) HCF.
Step-by-step explanation:
Given: The measure of steps of Nirmaljeet, Puneet and Raju are 240cm, 90cm, and 120cm.
To find :
a. The minimum distance of shop from where they start to walk together.
b. The number of common steps covered by all of them.
c. The relation between LCM and HCF.
Solution:
(a) since measure of steps of Nirmaljeet, Puneet and Raju are given, to find the minimum distance we have to find the Least Common Multiples of all the three measures 240cm, 90cm, 120cm.
LCM:
LCM denotes the least common factor or multiple of any two or more given integers.
Multiples of 240 =240,480,720,960,....
Multiples of 90 = 90, 180, 270,360,450,540,630,720,...
Multiples of 120 = 120,240, 360,480,600,720, 840,....
Here common multiple which is the least is 720.
LCM(240,90,120) = 720. option(1)
The minimum distance of shop from where they start to walk together, so that one can cover the distance in complete steps is 720cm.
(b) To find the number of common steps covered by all of them , we find the HCF of three numbers.
HCF:
HCF (Highest Common Factor) is the largest positive number that divides the given numbers, without any remainder. HCF is also called the Greatest Common Divisor (GCD).
factors of 240 = 2×2×2×2×3×5=2⁴×3×5
factors of 90 = 2×5×3×3 = 2×5×3²
factors of 120 =2×2×2×3×5 = 2³×3×5
highest common factor = 2×3×5 = 30
∴HCF(240,90,120) = 2×3×5 = 30.So option (2).
The number of common steps covered by all of them to reach the juice shop is 30.
(c )If a and b are two numbers, then the relation between LCM and HCF is , LCM(a, b)×HCF(a, b) = a × b.
option(
(d) A largest positive integer that divides given two positive integers is called the HCF.
So option (1) HCF.
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