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) 3
(b) 4
(c) 1
(d) 2
The correct answers to the above question in:
Answer: (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)
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Read more finding lcm Based Quantitative Aptitude Questions and Answers
Question : 1
The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?
a) 12
b) 8
c) 35
d) 24
Answer »Answer: (c)
LCM = 2 × 2 × 2 × 3 × 5
Hence, HCF = 4, 8, 12 or 24
According to question
35 cannot be H.C.F. of 120.
Question : 2
The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?
a) 48
b) 24
c) 60
d) 56
Answer »Answer: (c)
HCF of two numbers is 8.
This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60
Question : 3
The product of two numbers is 216. If the HCF is 6, then their LCM is
a) 60
b) 72
c) 36
d) 48
Answer »Answer: (c)
Let the numbers be 6x and 6y where x and y are prime to each other.
∴ 6x × 6y = 216
⇒ xy = $216/{6 × 6}$ = 6
∴ LCM = 6xy = 6 × 6 = 36
Question : 4
The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is
a) 144
b) 126
c) 238
d) 198
Answer »Answer: (b)
Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Second number =${HCF × LCM}/{First number} $
= ${18 ×378}/54$ = 126
Question : 5
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 : 6
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
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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