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 : 21 [SSC CGL Tier-I 2013]
Product of two co-prime numbers is 117. Then their L.C.M. is
a) 9
b) 117
c) 39
d) 13
Answer »Answer: (b)
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.
Question : 22 [SSC CGL Prelim 2008]
The product of two numbers is 4107. If the H.C.F. of the numbers is 37, the greater number is
a) 111
b) 185
c) 101
d) 107
Answer »Answer: (a)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
LCM = ${Product of two numbers}/ {HCF}$ = $4107/37$ = 111
Obviously, numbers are 111 and 37 which satisfy the given condition.
Hence, the greater number = 111
Question : 23
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) 90
b) 105
c) 45
d) 60
Answer »Answer: (c)
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
Question : 24
The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is
a) 2
b) 1
c) 4
d) 3
Answer »Answer: (a)
HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160
⇒ xy = $2160/{12 × 12} $
= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Question : 25
The H.C.F. and L.C.M. of two 2- digit numbers are 16 and 480 respectively. The numbers are :
a) 60, 72
b) 40, 48
c) 80, 96
d) 64, 80
Answer »Answer: (c)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
H.C.F. of the two 2-digit numbers = 16
Hence, the numbers can be expressed as 16x and 16y, where x and y are prime to each other.
Now,
First number × second number = H.C.F. × L.C.M.
⇒ 16x × 16y = 16 × 480
⇒ xy = ${16× 480}/{16 ×16}$ = 30
The possible pairs of x and y, satisfying the condition xy = 30 are : (3, 10), (5, 6), (1, 30), (2, 15)
Since the numbers are of 2-digits each.
Hence, admissible pair is (5, 6)
∴ Numbers are : 16 × 5 = 80 and 16 × 6 = 96
IMPORTANT quantitative aptitude EXERCISES
model 1 Basic formula of LCM & HCF Shortcuts »
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Click to Start..LCM & HCF Shortcuts and Techniques with Examples
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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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