model 1 Basic formula of LCM & HCF Practice Questions Answers Test with Solutions & More Shortcuts
LCM & HCF PRACTICE TEST [5 - EXERCISES]
model 1 Basic formula of LCM & HCF
model 2 find lcm of numbers
model 3 find hcf of numbers
model 4 addition, subtraction, multiplication and division with lcm & hcf
model 5 lcm & hcf vs ratios
Question : 11
The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.
a) 240
b) 204
c) 320
d) 260
Answer »Answer: (a)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We have,
First number × second number = LCM × HCF
∴ Second number = ${1920 × 16}/128$ = 240
Question : 12 [SSC CGL Prelim 2004]
The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is :
a) 299
b) 276
c) 322
d) 345
Answer »Answer: (c)
Let the numbers be 23x and 23y where x and y are co-prime.
∴ LCM = 23 xy
As given,
23xy = 23 × 13 × 14
∴ x = 13, y = 14
∴ The larger number = 23y
= 23 × 14 = 322
Question : 13
The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is :
a) 75
b) 50
c) 100
d) 65
Answer »Answer: (a)
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
Question : 14
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) 91
b) 78
c) 117
d) 104
Answer »Answer: (a)
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
Question : 15 [SSC Multi-Tasking Staff 2011]
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) 25
b) 5
c) 125
d) 100
Answer »Answer: (a)
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
IMPORTANT quantitative aptitude EXERCISES
model 1 Basic formula of LCM & HCF Shortcuts »
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model 1 Basic formula of LCM & HCF
Defination & Shortcuts … -
model 2 find lcm of numbers
Defination & Shortcuts … -
model 3 find hcf of numbers
Defination & Shortcuts … -
model 4 addition, subtraction, multiplication and division with lcm & hcf
Defination & Shortcuts … -
model 5 lcm & hcf vs ratios
Defination & Shortcuts …
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