Advertisements
Advertisements
Question
If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is
Options
203400
194400
198400
205400
Solution
Let the HCF be x and the LCM of the two numbers be y.
It is given that the sum of the HCF and LCM is 1260
x + y = 1260 …… (i)
And, LCM is 900 more than HCF.
y = x + 900 …… (ii)
Substituting (ii) in (i), we get:
`x + x + 900 = 1200`
`2x +900=1260`
`2x = 1260 -900`
`2x = 360`
x = 180
Substituting x = 180 in (ii), we get:
y = 180 + 900
y = 1080
We also know that the product the two numbers is equal to the product of their LCM and HCF
Thus the product of the numbers
= 194400(180)
= 194400
Hence, the correct choice is (b).
APPEARS IN
RELATED QUESTIONS
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.
Prove that the square of any positive integer of the form 5q + 1 is of the same form.
Using prime factorization, find the HCF and LCM of 144, 198 In case verify that HCF × LCM = product of given numbers.
Express each of the following integers as a product of its prime factors:
420
The LCM and HCF of two numbers are 180 and 6 respectively. If one of the numbers is 30, find the other number.
Prove that following numbers are irrationals:
The sum of two irrational number is an irrational number (True/False).
If two positive ingeters a and b are expressible in the form a = pq2 and b = p3q; p, q being prime number, then LCM (a, b) is
The smallest number by which \[\sqrt{27}\] should be multiplied so as to get a rational number is
Show that the cube of a positive integer of the form 6q + r, q is an integer and r = 0, 1, 2, 3, 4, 5 is also of the form 6m + r.
