[5 marks sum]

Question 15 Marks

Find the $L.C.M$. of the following group of numbers, using

the prime factor method and
the common division method

$34, 85$ and $51$

Answer

L.C.M. of 34,85 and 51
i. By prime factors
Prime factors of $34=2 \times 17=2^1 \times 17^1$
Prime factors of $85=5 \times 17=5^1 \times 17^1$
Prime factors of $51=3 \times 17=3^1 \times 17^1$
$\therefore$ L.C.M. of 34,85 and $51=2^1 \times 5^1 \times 3^1 \times 17=510$
ii. By common division method

$2$	$34,$	$85,$	$51$
$17$	$17,$	$85$	$51$
	$1,$	$5,$	$3$

$\therefore L.C.M$. of $34, 85$ and $51 = 2 x 17 x 5 x 3 = 510$

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Question 25 Marks

Find the $L.C.M$. of the following group of numbers, using

the prime factor method and
the common division method

$22, 121$ and $33$

Answer

L.C.M. of 22,121 and 33
i. By prime factors
Prime factors of $22=2 \times 11=2^1 \times 11^1$
Prime factors of $121=11 \times 11=11^2$
Prime factors of $33=3 \times 11=3^1 \times 11^1$
$\therefore$ L.C.M. of 22,121 and $33=2^1 \times 3^1 \times 11^1=726$
ii. By common division method

$2$	$22,$	$121,$	$33$
$11$	$11,$	$121,$	$33$
	$1,$	$11,$	$3$

$\therefore L.C.M$. of $22, 121$ and $33 = 2 x 11 x 11 x 3 = 726$

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Question 35 Marks

Find the $L.C.M.$ of the following group of numbers, using

the prime factor method and
the common division method

$14, 21$ and $98$

Answer

$L.C.M$. of $14, 21$ and $98$
i. By prime factors
Prime factors of $14=2 \times 7=2^1 \times 7^1$
Prime factors of $21=3 \times 7=3^1 \times 7^1$
Prime factors of $98=2 \times 7 \times 7=2^1 \times 7^2$
$\therefore L.C.M$. of $14,21$ and $98=2^1 \times 3^1 \times 7^2=294$
ii. By common division method

$2$	$14,$	$21,$	$98$
$7$	$7,$	$21,$	$49$
	$1,$	$3,$	$7$

$\therefore L.C.M.$ of $14, 21$ and $98 = 2 x 7 x 3 x 7 = 294$

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Question 45 Marks

Find the $L.C.M$. of the following group of numbers, using

the prime factor method and
the common division method

$100, 150$ and $200$

Answer

L.C.M. of 100,150 and 200
i. By prime factors
Prime factors of $100=2 \times 2 \times 5 \times 5=2^2 \times 5^2$
Prime factors of $150=2 \times 3 \times 5 \times 5=2^1 \times 3^1 \times 5^2$
Prime factors of $200=2 \times 2 \times 2 \times 5 \times 5=2^3 \times 5^2$
$\therefore$ L.C.M. of 100,150 and $200=2^3 \times 3^1 \times 5^2=600$
ii. By common division method

$2$	$100$,	$150,$	$200$
$2$	$50,$	$75,$	$100$
$5$	$25,$	$75,$	$50$
$5$	$5,$	$15,$	$10$
	$1,$	$3,$	$2$

$\therefore L.C.M$. of $100, 150$ and $200 = 2 x 2 x 5 x 5 x 3 x 2 = 600$

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Question 55 Marks

Find the L.C.M. of the following group of numbers, using

the prime factor method and
the common division method

18, 24 and 96

Answer

L.C.M. of 18, 24 and 96
i. By prime factors
Prime factors of 18 = 2 x 3 x 3
Prime factors of 24 = 2 x 2 x 2 x 3
Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3
L.C.M. = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
ii. By common division method
L.C.M. of 18, 24 and 96 = 2 x 2 x 2 x 3 x 3 x 4 = 288

2	18,	24,	96
2	9,	12,	48
2	9,	6,	24
3	9,	3,	12
	3,	1,	4

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Question 65 Marks

Out of 15, 16, 21 and 28, find out all the pairs of co-prime numbers.

Answer

The pair will be $15-16,16-21,21-28,15-28$ and $16-28,15-28$ and $16-28 \ldots$
The HCF of 15 and 16

and HCF of 21 and 28
HCF of 16 and 21 HCF of 13,28

HCF of 16, 28

From above it is clear that 15 and 16 are co-prime because the common factor is 1
Hence pairs 15 and 16, 16, 21, 15, 28 are the co-prime numbers.

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