Question

If the L.C.M. of two numbers is 315, then
which of the following numbers cannot
be the H.C.F. of the numbers?
(A) 315
(B) 105
(C) 63
(D) 84
(E) None of these

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Answer 1

Step-by-step explanation:

(a) 24

24 = 1 × 24 24 = 2 × 12 24 = 3 × 8

24 = 4 × 6 24 = 6 × 4

∴Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24

(b) 15

15 = 1 × 15 15 = 3 × 5 15 = 5 × 3

∴Factors of 15 are 1, 3, 5, and 15

(c) 21

21 = 1 × 21 21 = 3 × 7 21 = 7 × 3

∴Factors of 21 are 1, 3, 7, and 21

(d) 27

27 = 1 × 27 27 = 3 × 9 27 = 9 × 3

∴Factors of 27 are 1, 3, 9, and 27

(e) 12

12 = 1 × 12 12 = 2 × 6 12 = 3 × 4 12 = 4 × 3

∴Factors of 12 are 1, 2, 3, 4, 6, and 12

(f) 20

20 = 1 × 20 20 = 2 × 10 20 = 4 × 5 20 = 5 × 4

∴Factors of 20 are 1, 2, 4, 5, 10, and 20

(g) 18

18 = 1 × 18 18 = 2 × 9 18 = 3 × 6 18 = 6 × 3

∴Factors of 18 are 1, 2, 3, 6, 9, and 18

(h) 23

23 = 1 × 23 23 = 23 × 1

∴ Factors of 23 are 1 and 23

(i) 36

36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9

36 = 6 × 6

∴Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36

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