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HCF-LCM Word Problem examples ( Enter your problem )

 Problem : 1 / 11 [ HCF_LCM ]       Enter your problem 1. The HCF of two nos is 14 and their LCM is 11592 . If one of the nos is 504 , find the other? Solution: "Here, HCF"=14, "LCM"=11592, "No1"=504 and "No2"=?"No1" * "No2" = "HCF" * "LCM""No2 "= ( "HCF" * "LCM" ) / ("No1") = ( 14 * 11592 ) / 504 = 322.

Problem : 2 / 11 [ HCF_LCM ]       Enter your problem
2. Find the largest no which can exactly divide 513,783,1107 .
Solution: "Required number" = "HCF of " 513,783,1107 = 27.

Find HCF of (513,783)

 1

513|
 7 8 3
|
 5 1 3

 1
|

|
 2 7 0
|
 5 1 3
|
 2 7 0

 1
|

|
 2 4 3
|
 2 7 0
|
 2 4 3

 9
|

|
 2 7
|
 2 4 3
|
 2 4 3
|
|
 0

HCF of (513, 783) = 27

Now find HCF of (27,1107)

 4 1

27|
 1 1 0 7
|
 1 0 8
|
|
 2 7
|
 2 7
|
|
 0

HCF of (27, 1107) = 27

:. HCF of given numbers (513,783,1107) = 27

Problem : 3 / 11 [ HCF_LCM ]       Enter your problem
3. Find the smallest no exactly divisible by 12,15,20,27 .
Solution: "Required number" = "LCM of " 12,15,20,27 = 540.

 2 12 15 20 27 2 6 15 10 27 3 3 15 5 27 3 1 5 5 9 3 1 5 5 3 5 1 5 5 1 1 1 1 1

LCM of 12,15,20,27 = 2 × 2 × 3 × 3 × 3 × 5 = 540

Problem : 4 / 11 [ HCF_LCM ]       Enter your problem
4. Find the least no which when divided by 6,7, 8, 9,12 leaves the same remainder 2 in each case.
Solution: "Required number" = ( "LCM of " 6,7,8,9,12 ) + 2 = 504 + 2 = 506.

 2 6 7 8 9 12 2 3 7 4 9 6 2 3 7 2 9 3 3 3 7 1 9 3 3 1 7 1 3 1 7 1 7 1 1 1 1 1 1 1 1

LCM of 6,7,8,9,12 = 2 × 2 × 2 × 3 × 3 × 7 = 504

Problem : 5 / 11 [ HCF_LCM ]       Enter your problem
5. Find the largest no which divides 77 , 147 , 252 to leave the same remainder in each case.
Solution: "Required number" = "HCF of " ( 147 - 77 ), ( 252 - 147 ), ( 252 - 77 )

= "HCF of " 70, 105, 175 = 35.

Factor of 70,105,175 are as follows...

70 = 2 × 5 × 7
105 = 3 × 5 × 7
175 = 5 × 5 × 7

 2 70 5 35 7 7 1

 3 105 5 35 7 7 1

 5 175 5 35 7 7 1

HCF = 5 × 7 = 35

HCF of 70,105,175 is 35

Problem : 6 / 11 [ HCF_LCM ]       Enter your problem
6. Greatest no which can divide 1354 , 1806 and 2762 leaving the same remainder 10 in each case.
Solution: The number divides 1354 and leaves 10 as remainder
:. The number exactly divides 1354 - 10 = 1344

The number divides 1806 and leaves 10 as remainder
:. The number exactly divides 1806 - 10 = 1796

The number divides 2762 and leaves 10 as remainder
:. The number exactly divides 2762 - 10 = 2752

Now, we have to find HCF of 1344, 1796, 2752

Find HCF of (1344,1796)

 1

1344|
 1 7 9 6
|
 1 3 4 4

 2
|

|
 4 5 2
|
 1 3 4 4
|
 9 0 4

 1
|

|
 4 4 0
|
 4 5 2
|
 4 4 0

 3 6
|

|
 1 2
|
 4 4 0
|
 3 6
|
|
 8 0
|
 7 2

 1
|

|
 8
|
 1 2
|
 8

 2
|

|
 4
|
 8
|
 8
|
|
 0

HCF of (1344, 1796) = 4

Now find HCF of (4,2752)

 6 8 8

4|
 2 7 5 2
|
 2 4
|
|
 3 5
|
 3 2
|
|
 3 2
|
 3 2
|
|
 0

HCF of (4, 2752) = 4

:. HCF of given numbers (1344,1796,2752) = 4

:. Required number = HCF of 1344, 1796, 2752 = 4.

Problem : 7 / 11 [ HCF_LCM ]       Enter your problem
7. The greatest no that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder.
Solution: The number divides 1657 and leaves 6 as remainder
:. The number exactly divides 1657 - 6 = 1651

The number divides 2772 and leaves 5 as remainder
:. The number exactly divides 2772 - 5 = 2767

Now, we have to find HCF of 1651, 2767

Find HCF of (1651,2767)

 1

1651|
 2 7 6 7
|
 1 6 5 1

 1
|

|
 1 1 1 6
|
 1 6 5 1
|
 1 1 1 6

 2
|

|
 5 3 5
|
 1 1 1 6
|
 1 0 7 0

 1 1
|

|
 4 6
|
 5 3 5
|
 4 6
|
|
 7 5
|
 4 6

 1
|

|
 2 9
|
 4 6
|
 2 9

 1
|

|
 1 7
|
 2 9
|
 1 7

 1
|

|
 1 2
|
 1 7
|
 1 2

 2
|

|
 5
|
 1 2
|
 1 0

 2
|

|
 2
|
 5
|
 4

 2
|

|
 1
|
 2
|
 2
|
|
 0

:. HCF of given numbers (1651,2767) = 1

:. Required number = HCF of 1651, 2767 = 1.

Problem : 8 / 11 [ HCF_LCM ]       Enter your problem
8. The greatest no that will divide 290 , 460 , 552 leaving respectively 4 , 5 , 6 as remainder.
Solution: The number divides 290 and leaves 4 as remainder
:. The number exactly divides 290 - 4 = 286

The number divides 460 and leaves 5 as remainder
:. The number exactly divides 460 - 5 = 455

The number divides 552 and leaves 6 as remainder
:. The number exactly divides 552 - 6 = 546

Now, we have to find HCF of 286, 455, 546

Find HCF of (286,455)

 1

286|
 4 5 5
|
 2 8 6

 1
|

|
 1 6 9
|
 2 8 6
|
 1 6 9

 1
|

|
 1 1 7
|
 1 6 9
|
 1 1 7

 2
|

|
 5 2
|
 1 1 7
|
 1 0 4

 4
|

|
 1 3
|
 5 2
|
 5 2
|
|
 0

HCF of (286, 455) = 13

Now find HCF of (13,546)

 4 2

13|
 5 4 6
|
 5 2
|
|
 2 6
|
 2 6
|
|
 0

HCF of (13, 546) = 13

:. HCF of given numbers (286,455,546) = 13

:. Required number = HCF of 286, 455, 546 = 13.

 Problem : 9 / 11 [ HCF_LCM ]       Enter your problem 9. The product of HCF and LCM of 18 and 16 is Solution: Product of HCF and LCM = product of given numbers = 18 * 16 = 288.

 Problem : 10 / 11 [ HCF_LCM ]       Enter your problem 10. LCM of two nos is 14 times their HCF. The sum of LCM and HCF is 600 . If one no is 280 , then find the other no ? Solution: "LCM" = 14" HCF""LCM + HCF " = 600=> 14 " HCF + HCF " = 600=> 15 " HCF " = 600=> "HCF " = 600 / 15 = 40Here, "LCM" = 14 " HCF":. "LCM " = 14 * 40 = 560.:. "Other No " = ( "HCF" * "LCM" ) / ("Given No"} = ( 40 * 560 ) / 280 = 80.

Problem : 11 / 11 [ HCF_LCM ]       Enter your problem
11. Find the least number which is exactly divided by 28,36,45 when we add 19 to it
Solution: "Required number" = ( "LCM of " 28,36,45 ) - 19 = 1260 - 19 = 1241.

 2 28 36 45 2 14 18 45 3 7 9 45 3 7 3 15 5 7 1 5 7 7 1 1 1 1 1

LCM of 28,36,45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260