RD SHARMAS SOLUTIONS
REAL NUMBERS
(PART -1)
QUESTION 1
Find the LCM and HCF of the following pairs of integers and verify that LCM* HCF = product of the integers;
i) 26 and 91
ii)510 and 92
iii)336 and 54
ANSWER
To find ; LCM and HCF of the following integers
To verify; LCM*HCF = product of the numbers
i) 26 and 91
Let us find the factors of 26 and 91
26 = 2*13
91 = 7* 13
LCM of 26 and 91 =2*7*13
LCM of 26 and 91 =182
HCF of 26, and 91 = 182
we know that LCM*HCF = First number* Second number
182*13 = 26*91
2366 = 2366
Hence verified
ii) 510 and 92
Let us first find the factors of 510 and 92
510 = 2*3*5*7
92 =2*2*23
LCM of 510 and 92 =2*2*3*5*23*17
HCF of 510 and 92 =2
we know that, LCM* HCF =First Number*Second Number
23460*2 =510*92
46920= 46920
Hence verified
iii)336 and 54
Let us first find the factors of 336 = 2*2*2*2*3*3*3*7
54 = 2*3*3*3
LCM of 336 and 54 = 2*2*2*2*3*3*3*7
LCM of 336 and 54 =3024
HCF of 336 and 54 =6
we know that LCM*HCF =First Number*Second Number
3024*6 =336*54
18144 = 18144
Hence verified
QUESTION 2
Find the LCM and HCF of the following integers by prime factorization method
i) 12,15 and 21
ii) 17,23 and29
iii) 8,9 and 25
iv)40,36 and 126
v) 84,90 and 120
vi)24,15 and 36
ANSWERS
i)15,12 and 21
Let us find the factors of 15,12 and 21
15=5*3
12 =2*2*3
21=3*7
LCM =2*2*3*5*7
=420
HCF =3
ii) 17,23 and 29
Let us find the factors of 17,23 and 29
17= 1*17
23=1*23
29=1*29
LCM=17*23*29
=11339
HCF= 1
iii)8,9 and 25
Let us first find the factors of 8,9 and 25
8=2*2*2
9=3*3
25=5*5
LCM =2*2*3*3*5*5
=1800
HCF=1
iii)40,36 and 126
Let us find the factors of 40,36 and 126
40=2*2*2*5
36=2*2*3*3
126=2*3*3*7
LCM=2*2*3*3*2*5*7
=2520
HCF=2
iii)84,90 and 120
Let us find the factors of 84,90 and 120
84=2*2*3*7
90=2*3*3*5
120=2*2*2*3*5
LCM= 2*2*2*3*3*5*7
=2520
HCF=6
iv)24,15 and 36
Let us find the factors of 24,15 and 36
24=2*2*2*3
15=3*5
36=2*2*3*3
LCM=2*2*2*2*3*3*5
=360
HCF=3
QUESTION 3
Given that HCF(306,657) = 9, find the LCM(306,657)
ANSWER
HCF of two numbers 306 and 657 is 9
To find LCM OF The numbers
we know that
LCM*HCF = First Number* Second Number
LCM*9 =306*657
LCM =306*657/9
=22338
QUESTION 4
Can two numbers have 16 as their HCF and 380 as their LCM? Give reason?
ANSWER
To find; can two numbers have 16 as their HCF and 380 as their LCM
On dividing 380 by 16 we get 23 as quotient and 12 as the remainder
since LCM is not exactly divisible by HCF, two numbers cannot have 16 as their HCF and 380 as their LCM.
QUESTION 5
The HCF of two numbers is 145 and their LCM is 2175. If one number is 725,find the other?
ANSWER
Given,
LCM and HCF of two numbers 145 and 2175 respectively
if one number is 725
To find the other number
we know that
LCM*HCF = First Number*Second Number
2175*145 =725 * Second Number
LCM =2175*145 /725
=435
SUMMARY;
RD Sharma Class 10 Solutions
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