HCF_LCM Problems calculator

Problem : 1 [ HCF_LCM ] Solve this type of problem

1. The HCF of two numbers is 14 and their LCM is 11592 . If one of the numbers is 504 , find the other?
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A:	`"Here, HCF"=14, "LCM"=11592, "No1"=504 and "No2"=?` `"No1" * "No2" = "HCF" * "LCM"` `"No2 "= ( "HCF" * "LCM" ) / ("No1") = ( 14 * 11592 ) / 504 = 322`.

Problem : 2 [ HCF_LCM ] Solve this type of problem

2. Find the largest number which can exactly divide 513,783,1107 .

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`"Required number" = "HCF of " 513,783,1107 = 27`.

Find HCF of (513,783)

513

HCF of (513, 783) = 27

Now find HCF of (27,1107)

HCF of (27, 1107) = 27

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

Problem : 3 [ HCF_LCM ] Solve this type of problem

3. Find the smallest number exactly divisible by 12,15,20,27 .

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`"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 [ HCF_LCM ] Solve this type of problem

4. Find the least number which when divided by 6,7, 8, 9,12 leaves the same remainder 2 in each case.

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`"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 [ HCF_LCM ] Solve this type of problem

5. Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case.

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`"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 [ HCF_LCM ] Solve this type of problem

6. Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case.

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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)

1344

HCF of (1344, 1796) = 4

Now find HCF of (4,2752)

HCF of (4, 2752) = 4

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

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

Problem : 7 [ HCF_LCM ] Solve this type of problem

7. The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder.

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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)

1651

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

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

Problem : 8 [ HCF_LCM ] Solve this type of problem

8. The greatest number that will divide 290 , 460 , 552 leaving respectively 4 , 5 , 6 as remainder.

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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)

286

HCF of (286, 455) = 13

Now find HCF of (13,546)

HCF of (13, 546) = 13

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

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

Problem : 9 [ HCF_LCM ] Solve this type of problem

9. The product of HCF and LCM of 18 and 16 is
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A:	Product of HCF and LCM = product of given numbers `= 18 * 16 = 288`.

Problem : 10 [ HCF_LCM ] Solve this type of 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 ?
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A:	`"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 [ HCF_LCM ] Solve this type of problem

11. Find the least number which is exactly divided by 28,36,45 when we add 19 to it

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`"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