Practice Finding lcm - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) The product of two numbers is 2028 and their HCF is 13. The number of such pairs is
(a)
(b)
(c)
(d)
Here, HCF = 13
Let the numbers be 13x and 13y where x and y are Prime to each other.
Now, 13x × 13y = 2028
⇒ xy = ${2028}/{13×13}$ = 12
The possible pairs are : (1, 12), (3, 4), (2, 6)
But the 2 and 6 are not co-prime.
∴ The required no. of pairs = 2
Q-2) Product of two co-prime numbers is 117. Then their L.C.M. is
(a)
(b)
(c)
(d)
HCF of two-prime numbers = 1
∴ Product of numbers = their LCM = 117
117 = 13 × 9 where 13 & 9 are co-prime. L.C.M (13,9) = 117.
Q-3) The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is
(a)
(b)
(c)
(d)
Let the number be 15x and 15y, where x and y are co –prime.
∴ 15x × 15y = 6300
⇒ xy = $6300/{15 ×15}$ = 28
So, two pairs are (7, 4) and (14, 2)
Q-4) The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is :
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
∴ Second number = ${15 × 300}/60$ = 75
Q-5) The HCF and LCM of two numbers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is :
(a)
(b)
(c)
(d)
HCF = 13
Let the numbers be 13x and 13y.
Where x and y are co-prime.
∴ LCM = 13 xy
∴ 13 xy = 455
∴ xy = $455/13$ = 35 = 5 × 7
∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91
Q-6) The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the number is 100, then the other number is
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Let LCM be L and HCF be H, then L = 4H
∴ H + 4H = 125
⇒ 5H = 125
⇒ H = ${125}/5$ = 25
∴ L = 4 × 25 = 100
∴ Second number = ${L× H}/{First number}$
= ${100 ×25}/100$ = 25
Q-7) The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520
⇒ Second number =${4 × 520}/52$ = 40
Q-8) The H.C.F and L.C.M of two numbers are 12 and 336 respectively. If one of the number is 84, the other is
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336
∴ Second number = ${12 × 336}/84$ = 48
Q-9) The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is :
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225
∴ Second number = ${15 × 225}/75$ = 45
Q-10) The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is
(a)
(b)
(c)
(d)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We know that,
First number × Second number = LCM × HCF
⇒ Second number = ${16 × 160}/32$ = 80