[4 marks sum]

Question 14 Marks

Find the H.C.F. of $108$ and $450$ and use the H.C.F. obtained to find the L.C.M. of the given numbers.

Answer

Numbers are given: $108$ and $450$
H.C.F. of $108$ and $450= 18$

$\therefore \text { L.C.M. }=\frac{1 \text { st number } \times 2 \text { nd number }}{\text { H.C.F. }}$
$=\frac{108 \times 450}{18}=2700$

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Question 24 Marks

Find the L.C.M. of 48, 66 and 120

Answer

L.C.M. of 48, 66 and 120

2	48,	66,	120
2	24,	33,	60
2	12,	33,	30
3	6,	33,	15
	2,	11,	5

= 2 × 2 × 2 × 2 × 3 × 5 × 11 = 2640

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Question 34 Marks

Find the L.C.M. of 72, 80 and 252

Answer

L.C.M. 72, 80, 252

2	72,	80,	252
2	36,	40,	126
2	18,	20,	63
3	9,	10,	63
3	3,	10,	21
	1,	10,	7

= 2 × 2× 2 × 3 × 3 × 10 × 7 = 5040

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Question 44 Marks

Find the H.C.F. of 36, 54 and 138

Answer

H.C.F. of 36, 54 and 138 = 6

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Question 54 Marks

Find the H.C.F. of 108, 288 and 420

Answer

$
\text { H.C.F. of } 108,288,420=12
$

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Question 64 Marks

Find the smallest number which, on being decreased by 3, is completely divisible by 18, 36, 32 and 27.

Answer

LCM of 18, 36, 32 and 27

2	18,	36,	32,	27
2	9,	18,	16,	27
3	9,	9,	8,	27
3	3,	3,	8,	9
	1,	1,	8,	3

∴ L.C.M. = 2 x 2 x 3 x 3 x 3 x 8 = 864
∴ The required number = 864 + 3 = 867

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Question 74 Marks

Find the smallest number which, when increased by one is exactly divisible by 12, 18, 24, 32 and 40

Answer

L.C.M. of given numbers

2	12,	18,	24,	32,	40
2	6,	9,	12,	16,	20
2	3,	9,	6,	8,	10
3	3,	9,	3,	4,	5
	1,	3,	1,	4,	5

∴ L.C.M. = 2 x 2 x 2 x 3 x 3 x 4 x 5 = 1440 = One increasing
∴ The required number = 1440 - 1 = 1439

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Question 84 Marks

Find the smallest number which, when divided by 12, 15, 18, 24 and 36 leaves no remainder

Answer

The least number which is exactly divisible by each given number is their L.C.M. Required number L.C.M. of 12, 15, 18, 24 and 36.

2	12,	15,	18,	24,	36
2	6,	15,	9,	12,	18
3	3,	15,	9,	6,	9
3	1,	5,	3,	2,	3
	1,	5,	1,	2,	1

∴ L.C.M. = Least required number
= 2 x 2 x 3 x 3 x 5 x 2 = 360
Hence, the least required number = 360

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Question 94 Marks

Find the greatest no. that will divide $93, 111,$ and $129,$ leaving remainder $3$ in each case.

Answer

Since Remainder is $3$ in each case numbers are
$93-3=90$
$111-3=108 $
$129-3=126$
Required number will be HCF of $90,108$ and $126$ HCF of $90$ and $108$

HCF of $18$ and $126$

$\therefore \text { The greatest number will be }=18$

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Question 104 Marks

Find the greatest number that divides each of 180, 225 and 315 completely

Answer

The greatest number that divides 180,225 and 315 will be HCF of $180,225,315$ Let us first find HCF of 180 and 225

Since the third number is 315 , and HCF obtained above is 45 , find the HCF of 315 and 45.

$
\therefore \text { HCF of given number } 80,225 \text { and } 315=45
$

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Question 114 Marks

Using the division method, find the H.C.F. of the following:
32, 56 and 46

Answer

32, 56 and 46

Since last division is 2
$\therefore$ H.C.F. of 32,56 and $46=2$

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MATHS [4 marks sum]

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