In our daily life we all see traffic lights. A traffic controller set the timings of
traffic signals in such a way that all lights are not green at the same time,
especially not in rush hours. To maintain the smooth flow of traffic, the timings
of nearby places in the same area are taken to calculate the traffic stops. The
duration of traffic signal can be increased or decreased at different times. There
are two traffic lights on a particular highway which show green light at a duration
of 90 seconds and 144 seconds, respectively.
) Find the HCF between two green lights.
(a) 20 (b) 18
( c) 16 (d) 22
(ii) Find the LCM between two green lights.
(a) 720 (b) 730
(c ) 540 (d) 640
(iii) Factor tree is used for determining the
(a) HCF (b) LCM
(c)Prime factors (d) None of these
(iv) Identify the correct option.
(a) HCF (a, b) × LCM (a , b) =
(b) ( ,)
( ,)
=
(c) HCF (a, b) × LCM (a , b) = a - b
(d)HCF (a , b) × LCM(a , b) = ab
(v) Numbers that do not have no common factors other than 1, are called
(a) Coprime numbers
(b)Prime numbers
(c) Both prime and coprime numbers
(d)Composite numbers
Answers
Solution :-
Prime factors of 90 and 144 :-
→ 90 = 2 * 3 * 3 * 5
→ 144 = 2 * 2 * 2 * 2 * 3 * 3
so,
→ HCF = 2 * 3 * 3 = 18 . (Ans.i) (Option b) .
→ LCM = 2 * 2 * 2 * 2 * 3 * 3 * 5 = 720 . (Ans.ii) (Option a) .
Answer iii) :-
- A factor tree is used to determine the prime factors of a natural number greater than one. (Option c).
Answer iv) :-
- (d) HCF (a , b) × LCM(a , b) = ab .
Answer v) :-
- Numbers that do not have no common factors other than 1, are called Prime Number . (Option b).
Answer:
traffic signals in such a way that all lights are not green at the same time,
especially not in rush hours. To maintain the smooth flow of traffic, the timings
of nearby places in the same area are taken to calculate the traffic stops. The
duration of traffic signal can be increased or decreased at different times. There
are two traffic lights on a particular highway which show green light at a duration
of 90 seconds and 144 seconds, respectively.
) Find the HCF between two green lights.
(a) 20 (b) 18
( c) 16 (d) 22
(ii) Find the LCM between two green lights.
(a) 720 (b) 730
(c ) 540 (d) 640
(iii) Factor tree is used for determining the
(a) HCF (b) LCM
(c)Prime factors (d) None of these
(iv) Identify the correct option.
(a) HCF (a, b) × LCM (a , b) =
(b) ( ,)
( ,)
=
(c) HCF (a, b) × LCM (a , b) = a - b
(d)HCF (a , b) × LCM(a , b) = ab
(v) Numbers that do not have no common factors other than 1, are called
(a) Coprime numbers
(b)Prime numbers
(c) Both prime and coprime numbers
(d)Composite numbers
Step-by-step explanation: