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HCF and LCM Questions and answers pdf in hindi.

What is HCF and LCM ?

LCM means least common multiple and HCF is Highest Common Factor.

HCF and LCM : Definition: LCM is a that number is the least number which is exactly divide by each one of the given numbers.




Now we understand through solve some problems.

hcf and lcm problems for competitive exams

Q.1, Find out the LCM of 3 & 4.
Solve:
now we break both number in मल्टीप्लेस
= 3 x 1 x 2 x 2 = 12 Ans.
Q.2, Find out the LCM of 12, 36, 45, 60 .

Solve:-
2 12,36,45,60
3 6,  18, 45, 30
3 2,   6,   15, 10
2 2,   2,   5,   10
5 1,   1,   5,   10

1,   1,  1,  2
Q. 6, दो संख्याओ का महत्तम समापवर्तक तथा लघुतम समापवर्तक क्रमश: 8 तथा 48 है । यदि इनमे से एक संख्या 24 है तो दुसरी संख्या ज्ञात करें ?
Solve: माना कि दुसरी संख्या = x है ।
(पहली संख्या X दुसरी संख्या ) = म स X ळ ष
=> २४ X x  = 8 X 48
=> x=(8 x 48)/24
x =16 Ans.
Q. 7, If two numbers are HCF and LCM 11 and 7700, and one number is 275, then find the second number?
Solve:
Suppose second number = X
Then, (275 x x) = 11 x 7700
=> 275 x = 11 x 7700
=> x = 11 x 7700/275
x = 308 ाँस.
Q. 8, 12 के दो गुणजो का LCM 1056 है। यदि इनमें से एक संख्या 132 है तो दुसरी संख्या क्या होगा ?
Solve:
एक संख्या = 132 = 12 x 11
let to be other number is = x
तब
LCM = 132 x
by the question
=> 132 x = 1056
=> x= 1056/132
x = 8 Ans
इसलिए दुसरी संख्या = 12 x 8 = 96 Ans.
Q. 9 , दो संख्यांए 3:4 के अनुपात में है, और इनका LCM 84 है, तो इनमे से बडी संख्या ज्ञा करें ?
Solve :
माना कि अनुपातिक राशि = x
=> संख्या= 3 x और 4 x होगी
=> LCM =12 x
=> 12 x = 84
=> x = 84/12
x= 7
=> प्र्थम संख्या= 3 x = 3 X 7 =21
=> दुसरी संख्या = 4 x =4 X 7 =28

Q. 11,  दो संख्याओ का योगफ़ल 36 है, यदि इनका HCF 3 तथा LCM 105 है तो इन संख्याओ का व्युत्क्र्म का योगफ़ल निकालें ?
Solution:
माना कि संख्याएं x तथा y है
=> x +y = 36 तथा => xy = ( 3×105)=315
=> 1/x + 1/y = (x +y)/xy =36/315=4/35 ाँस.
Q.12, तीन अंकों वाली दो संख्याओ का म.स.17 है, तथा ल.स.714 है, तो इन सबका योगफ़ल निकालें ?
Solve :-
माना कि ये संख्याएं क्रमश: 17a तथा 17b है,
=> 17a x 17b = 17 x 714
=> ab = 714/17
=> ab = 42
=> ab = 6 x 7
=> एक संख्या = 17 x 6 =102
=> दुसरी संख्या = 17 x 7 = 119
इनका योगफ़ल = 102 + 119 = 221 Ans.




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