1. Calculations
H.C.F.
L.C.M.
using Prime Factors
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2. Round 1
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3. Find the H.C.F. and the L.C.M. of 24 and 36
= 2 x 2 x 2 x 3
= 23 x 31 12 36
= 2 x 2 x 3 x 3
= 22 x 32 2 2 6 18 2 9 2 3 2 3 3 3 1 3 1
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4. Find the H.C.F. and the L.C.M. of 24 and 36
= 2 x 2 x 2 x 3
= 23 x 31 36
= 2 x 2 x 3 x 3
= 22 x 32
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5. 12 H.C.F. = 22 x 31 = Find the H.C.F. and the L.C.M. of 24 and 36 24
= 2 x 2 x 2 x 3
= 23 x 31 36
= 2 x 2 x 3 x 3
= 22 x 32 12
H.C.F. =
22 x 31 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
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6. 72 L.C.M. = 23 x 32 = Find the H.C.F. and the L.C.M. of 24 and 36 24
= 2 x 2 x 2 x 3
= 23 x 31 36
= 2 x 2 x 3 x 3
= 22 x 32 72
L.C.M. =
23 x 32 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
The L.C.M is given by the product of:
All prime factors
with the highest power
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7. Round 2
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8. Find the H.C.F. and the L.C.M. of 30 and 48
= 2 x 3 x 5
= 21 x 31 x 51 15 48
= 2 x 2 x 2 x 2 x 3
= 24 x 31 2 3 5 24 2 5 1 2 12 2 6 2 3 3 1
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9. Find the H.C.F. and the L.C.M. of 30 and 48
= 2 x 3 x 5
= 21 x 31 x 51 48
= 2 x 2 x 2 x 2 x 3
= 24 x 31
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10. 6 H.C.F. = 21 x 31 = Find the H.C.F. and the L.C.M. of 30 and 48 30
= 2 x 3 x 5
= 21 x 31 x 51 48
= 2 x 2 x 2 x 2 x 3
= 24 x 31 6
H.C.F. =
21 x 31 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
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11. 240 L.C.M. = 24 x 31 x 51= Find the H.C.F. and the L.C.M. of 30 and 48
= 2 x 2 x 2 x 2 x 3
= 24 x 31
240
L.C.M. =
24 x 31 x 51=
The H.C.F is given by the product of:
Common prime factors
with the lowest power
The L.C.M is given by the product of:
All prime factors
with the highest power
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12. Round 3
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13. Find the H.C.F. and the L.C.M. of 60 and 72
= 2 x 2 x 3 x 5
= 22 x 31 x 51 30 72
= 2 x 2 x 2 x 3 x 3 2
= 23 x 32 2 15 36 2 3 5 2 18 2 9 5 1 3 3 3 1
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14. Find the H.C.F. and the L.C.M. of 60 and 72
= 2 x 2 x 3 x 5
= 22 x 31 x 51 72
= 2 x 2 x 2 x 3 x 3
= 23 x 32
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15. 12 H.C.F. = 22 x 31 = Find the H.C.F. and the L.C.M. of 60 and 72 60
= 2 x 2 x 3 x 5
= 22 x 31 x 51 72
= 2 x 2 x 2 x 3 x 3
= 23 x 32 12
H.C.F. =
22 x 31 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
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16. 360 L.C.M. = 23 x 32 x 51= Find the H.C.F. and the L.C.M. of 60 and 72
= 2 x 2 x 3 x 5
= 22 x 31 x 51 72
= 2 x 2 x 2 x 3 x 3
= 23 x 32
360
L.C.M. =
23 x 32 x 51=
The H.C.F is given by the product of:
Common prime factors
with the lowest power
The L.C.M is given by the product of:
All prime factors
with the highest power
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17. Round 4
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18. Find the H.C.F. and the L.C.M. of 48 and 120
= 2 x 2 x 2 x 2 x 3
= 24 x 31 24
120
= 2 x 2 x 2 x 3 x 5 2
= 23 x 31 x 51 2 12 60 2 2 6 2 30 2 15 2 3 3 5 3 1 5 1
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19. Find the H.C.F. and the L.C.M. of 48 and 120
= 2 x 2 x 2 x 2 x 3
= 24 x 31
120
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51
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20. 24 H.C.F. = 23 x 31 = Find the H.C.F. and the L.C.M. of 48 and 120 48
= 2 x 2 x 2 x 2 x 3
= 24 x 31
120
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51 24
H.C.F. =
23 x 31 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
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21. Find the H.C.F. and the L.C.M. of 48 and 120
= 2 x 2 x 2 x 2 x 3
= 24 x 31
120
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51
240
L.C.M. =
24 x 31 x 51=
The H.C.F is given by the product of:
Common prime factors
with the lowest power
The L.C.M is given by the product of:
All prime factors
with the highest power
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22. Round 5
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23. Find the H.C.F. and the L.C.M. of 120 and 168
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51 60
168
= 2 x 2 x 2 x 3 x 7 2
= 23 x 31 x 71 2 30 84 2 2 15 2 42 2 21 3 5 3 7 5 1 7 1
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24. Find the H.C.F. and the L.C.M. of 120 and 168
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51
168
= 2 x 2 x 2 x 3 x 7
= 23 x 31 x 71
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25. Find the H.C.F. and the L.C.M. of 120 and 168
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51
168
= 2 x 2 x 2 x 3 x 7
= 23 x 31 x 71 24
H.C.F. =
23 x 31 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
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26. Find the H.C.F. and the L.C.M. of 120 and 168
= 2 x 2 x 2 x 3 x 5
= 23 x 31 x 51
168
= 2 x 2 x 2 x 3 x 7
= 23 x 31 x 71
840
L.C.M. =
23 x 31 x 51 x 71 =
The H.C.F is given by the product of:
Common prime factors
with the lowest power
The L.C.M is given by the product of:
All prime factors
with the highest power
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27. © T Madas