Practice Set 14
1. Choose the right option.
(i) The HCF of 120 and 150 is
(1) 30 (2) 45 (3) 20 (4) 120
(ii) The HCF of this pair of numbers is not 1.
(1) 13, 17 (2) 29, 20 (3) 40, 20 (4) 14,
2. Find the HCF and LCM.
(i) 14, 28 (ii) 32, 16 (iii) 17, 102, 170 (iv)
. Find the LCM.
(1) 36, 42 (ii) 15, 25, 30 (iii) 18, 42, 48
Find the smallest number which when divided
Answers
Answer:
1i) Option 1
ii) Option 3
2i) H.C.F- 14, L.C.M-28
ii) H.C.F- 16, L.C.M-32
iii) H.C.F- 17, L.C.M-510
3i) 252
ii) 150
iii) 1008
Step-by-step explanation:
When two or more numbers are exactly divisible by one greatest number , that greatest number is called highest common factor or H.C.F of those numbers.
Least Common Multiple is the smallest number which is exactly divisible by two or more numbers in the question.
i) By prime factorization method we can find out the H.C.F of 120 and 150.
2)120,150
________
5)60,75
________
3)12,15
________
4,5
Therefore the H.C.F of 120 and 150 is = 2*5*3
=30 (option 1)
ii) Option 3
When doing prime factorization of 40 and 20, we get
2)40,20
______
2)20,10
______
5)10,5
______
2,1
So, 2*2*5=20 is the H.C.F of 40 and 20 , not 1.
2i) H.C.F of 14,28
2)14,28
_____
7)7,14
_____
1,2
Therefore H.C.F of 14 and 28 is 2*7=14
L.C.M of 14,28
2)14,28
_____
7)7,14
_____
1,2
Therefore L.C.M of 14 and 28 is 2*7*1*2=28
ii) H.C.F of 32,16
2)32,16
______
2)16,8
______
2)8,4
______
2)4,2
______
2,1
Therefore H.C.F of 32 and 16 is 2*2*2*2=16
L.C.M of 32,16
2)32,16
______
2)16,8
______
2)8,4
______
2)4,2
______
2,1
Therefore L.C.M of 32 and 16 is 2*2*2*2*2=32
iii) H.C.F of 17,102,170
17)17,102,170
____________
1,6,10
Therefore H.C.F of 17,102,170= 17
L.C.M of 17,102,170
17)17,102,170
____________
2)1,6,10
____________
3,5
Therefore L.C.M of 17,102,170= 17*2*3*5=510
3i) L.C.M of 36, 42
2)36,42
_______
3)18,21
_______
6,7
Therefore L.C.M of 36, 42= 2*3*6*7
=252
ii) L.C.M of 15, 25, 30
5)15,25,30
__________
3)3,5,6
_________
1,5,2
Therefore L.C.M of 15, 25, 30= 5*3*1*5*2
= 150
iii) L.C.M of 18, 42, 48
2)18, 42, 48
___________
3)9,21,24
___________
3,7,8
Therefore L.C.M of 18, 42, 48 =2*3*3*7*8
=1008
Answer:
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Step-by-step explanation:
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