model 1 Basic formula of LCM & HCF Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on LCM & HCF topic of quantitative aptitude
(a) 90
(b) 105
(c) 45
(d) 60
The correct answers to the above question in:
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
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Read more finding lcm Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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
Question : 3
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) 80
b) 48
c) 112
d) 96
Answer »Answer: (a)
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
Question : 4
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 : 5
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 : 6
LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is
a) 584
b) 297
c) 216
d) 189
Answer »Answer: (b)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Second number = ${H.C.F.× L.C.M.}/{First Number}$
= ${27 × 2079}/189$ = 297
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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