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HCF-LCM Word Problem examples ( Enter your problem )
 
  1. Example-1
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1. Example-1

Problem : 1 / 11 [ HCF_LCM ]       Enter your problem
1. The HCF of two numbers is 14 and their LCM is 11592 . If one of the numbers 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 number which can exactly divide 513,783,1107 .
Solution: `"Required number" = "HCF of " 513,783,1107 = 27`.

Find HCF of (513,783)
  
1
  
513|
783
 |
513
 
1
 |
 
 |
270
|
513
|
270
 
1
|
 
|
243
|
270
|
243
 
9
|
 
|
27
|
243
|
243
|
|
0

HCF of (513, 783) = 27

Now find HCF of (27,1107)
  
41
  
27|
1107
 |
108 
 |
 |
27
 |
27
 |
 |
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 number exactly divisible by 12,15,20,27 .
Solution: `"Required number" = "LCM of " 12,15,20,27 = 540`.

212152027
26151027
3315527
31559
31553
51551
 1111

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 number 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`.

2678912
237496
237293
337193
317131
717111
 11111

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 number 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

270
535
77
 1
 
3105
535
77
 1
 
5175
535
77
 1

HCF = 5 × 7 = 35

HCF of `70,105,175` is `35`

Problem : 6 / 11 [ HCF_LCM ]       Enter your problem
6. Greatest number which can divide 1354 , 1806 , 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|
1796
 |
1344
 
2
 |
 
 |
452
|
1344
|
904
 
1
|
 
|
440
|
452
|
440
 
36
|
 
|
12
|
440
|
36 
|
|
80
|
72
 
1
|
 
|
8
|
12
|
8
 
2
|
 
|
4
|
8
|
8
|
|
0

HCF of (1344, 1796) = 4

Now find HCF of (4,2752)
  
688
  
4|
2752
 |
24  
 |
 |
35 
 |
32 
 |
 |
32
 |
32
 |
 |
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 number 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|
2767
 |
1651
 
1
 |
 
 |
1116
|
1651
|
1116
 
2
|
 
|
535
|
1116
|
1070
 
11
|
 
|
46
|
535
|
46 
|
|
75
|
46
 
1
|
 
|
29
|
46
|
29
 
1
|
 
|
17
|
29
|
17
 
1
|
 
|
12
|
17
|
12
 
2
|
 
|
5
|
12
|
10
 
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 number 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|
455
 |
286
 
1
 |
 
 |
169
|
286
|
169
 
1
|
 
|
117
|
169
|
117
 
2
|
 
|
52
|
117
|
104
 
4
|
 
|
13
|
52
|
52
|
|
0

HCF of (286, 455) = 13

Now find HCF of (13,546)
  
42
  
13|
546
 |
52 
 |
 |
26
 |
26
 |
 |
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 numbers is 14 times their HCF. The sum of LCM and HCF is 600 . If one number is 280 , then find the other number ?
Solution: `"LCM" = 14" HCF"`

`"LCM + HCF " = 600`

`=> 14 " HCF + HCF " = 600`

`=> 15 " HCF " = 600`

`=> "HCF " = 600 / 15 = 40`

Here, `"LCM" = 14 " HCF"`

`:. "LCM " = 14 * 40 = 560`.

`:. "Other number " = ( "HCF" * "LCM" ) / ("Given number"} = ( 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`.

2283645
2141845
37945
37315
5715
7711
 111

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


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