Multiple choice

If the L.C.M. of two numbers 240 and 360 is 720, find their H.C.F.

  1. 360

  2. 240

  3. 120

  4. 60
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C Correct answer
Explanation

L.C.M. $\times$ H.C.F. = Product of two numbers 720 $\times$ H.C.F. = 240 $\times$ 360 H.C.F. = $\frac{240 \times 360}{720}$           = 120 Alternatively, H.C.F. = Product of the smallest powers of each common prime factor in the numbers

2 240
2 120
2 60
2 30
3 15
  5

  ||| |---|---| | 2| 360| | 2| 180| | 2| 90| | 3| 45| | 3| 15| | | 5|

The prime factorisation of 240 = 24 $\times$ 31 $\times$ 51 The prime factorisation of 360 = 23 $\times$ 32 $\times$ 51 $\therefore$ H.C.F. = 23 $\times$ 3 $\times$ 5 = 8 $\times$15 = 120

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