Home > Word Problems calculators > HCF-LCM Word Problem example

HCF-LCM Word Problem examples ( Enter your problem )

 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|
 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 number 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 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.

 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 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

 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 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|
 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 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|
 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 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|
 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 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 = 40Here, "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.

 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

Copyright © 2019. All rights reserved. Terms, Privacy

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more