Sol.
Find the LCM and HCF of the following pairs of integers and verify that
LCM × HCF = Product of the two numbers.
Q.2
(ii) 510 and 12
510
510
255
85
2
3
5
17
17
1
=
×
3
×
5
×
17
12
12
6
3
2
2
3
1
=
22
×
3
HCF
(510,
12)
=
2 × 3 = 6
(Product of common factors raised to least power)
LCM
(510,
12)
=
22
×
3
×
5
×
17
1020
=
…(Product of all the prime factors
raised to highest power)
Verification :
1020
=
×
6
=
6120
Product of the two numbers
510
=
×
12
=
6120
∴
HCF
×
LCM
=
Product of the two numbers
HCF
×
LCM
2
Exercise 1.2
Sol.
(iii) 336 and 54
336
336
168
84
2
2
2
42
2
21
=
×
×
7
54
54
27
9
2
3
3
3
=
×
33
HCF
(336,
54)
=
2 × 3 = 6
(Product of common factors raised to least power)
LCM
(336,
54)
=
24
×
33
×
7
3024
=
…(Product of all the prime factors
raised to highest power)
Verification :
6
=
×
3024
=
18144
Product of the two numbers
336
=
×
54
=
18144
∴
HCF
×
LCM
=
Product of the two numbers
HCF
×
LCM
24
3
7
3
7
1
3
1
2
Find the LCM and HCF of the following pairs of integers and verify that
LCM × HCF = Product of the two numbers.
Q.2
Exercise 1.2