Advertisements
Advertisements
Question
The LCM and HCF of two rational numbers are equal, then the numbers must be
Options
prime
co-prime
composite
equal
Solution
Let the two numbers be a and b.
(a) If we assume that the a and b are prime.
Then,
HCF `(a,b)=1`
LCM `(a,b)=ab`
(b) If we assume that a and b are co-prime.
Then,
HCF `(a,b)=1`
LCM `(a,b)=ab`
(c) If we assume that a and b are composite.
Then,
HCF `(a,b)=1`or any other highest common integer
LCM `(a,b)=ab`
(d) If we assume that a and b are equal and consider a=b=k.
Then,
HCF `(a,b)=k`
LCM `(a,b)=k`
Hence the correct choice is (d).
APPEARS IN
RELATED QUESTIONS
Show that any positive odd integer is of the form 6q + 1 or, 6q + 3 or, 6q + 5, where q is some integer.
Prove that if a positive integer is of the form 6q + 5, then it is of the form 3q + 2 for some integer q, but not conversely.
A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?
What do you mean by Euclid’s division algorithm.
A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. it is to be paved with square tiles of the same size. Find the least possible number of such tiles.
Prove that following numbers are irrationals:
If 3 is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a + b, is
Prove that two consecutive positive integers are always co-prime
Show that cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3, for some integer m.
Show that the square of any odd integer is of the form 4q + 1, for some integer q.
