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The product of two co-primes is $104$ . Their L.C.M. should be:

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Important Questions on Rational Numbers

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Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Let

x, y, z

be positive integers such that

H C F (x, y, z) = 1

and

x^{2} + y^{2} = 2 z^{2} .

Which of the following statements are true?

I .

4

divides

x

4

divides

y

I I .

3

divides

x + y

3

divides

x - y

I I I .

5

divides

z (x^{2} - y^{2})

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

A, B, C have

152, 171

and

266

marbles, respectively. They decide to divide these marbles in parts such that all parts have the same number of marbles. Also, they cannot give or take the marbles. Find the minimum possible number of parts that can be made.

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the HCF of 3, 7 and 15.

(A) 7

(B) 15

(D) 1

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

What will be the HCF of $\frac{2}{3}, \frac{8}{9}$ and $\frac{64}{81}$ ?

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

What will be the Highest Common Factor of

4, 8

and

12 ?

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

The LCM and HCF of two numbers are

171360

and

14

respectively. If one of the numbers is

2142

then what is the second number?

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the number lying between

900

and

1000

which when divided by

38

and

57

leaves in each case a remainder

23

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

At a telephone exchange, three phones ring at intervals of

20

sec,

24

sec, and

30

sec. If they ring together at

11 : 25

am, when will they next ring together?

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

What is the Lowest Common Multiple of

2, 3

and

7

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

What is the value of half of the HCF of

36

and

144

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the number lying between

900

and

1000

, which when divided by

38

and

57

leaves in each case a reminder

23

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

12

is the highest common factor of '

a

' and '

b

'. '

a

' and '

b

' are integers and

a > b > 12

. What would be the minimum values of

(a, b)

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

The HCF of

\frac{2}{3}, \frac{8}{9}, \frac{10}{27}, \frac{32}{81}

is.

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the ratio of the LCM and the HCF of 5, 25 and 30.

(A) 1 : 6

(B) 30 : 1

(D) 6 : 1

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

x

is a prime number,

L C M

x

and its successive number would be:

MEDIUM

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the LCM of

\frac{25}{7}, \frac{15}{28}, \frac{20}{21}

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

The LCM of two numbers is $210$ . If their HCF is $35$ and one of the numbers is $105$ , find the other number:

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

What is the HCF of

\frac{15}{24}, \frac{12}{39} a n d \frac{40}{49}

EASY

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Find the G.C.F and L.C.M of $20$ and $28$ .

1. $20, 280$
2. $5, 280$
3. $10, 140$
4. $4, 140$

HARD

Mathematics>Arithmetic>Rational Numbers>Highest Common Factor and Least Common Multiple

Let

p (x) = x^{2} - 5 x + a & q (x) = x^{2} + 3 x + b

, where

a

and

b

are positive integers. Suppose

HCF (p (x), q (x)) = x - 1 & k (x) = LCM (p (x), q (x))

. If the coefficient of the highest degree term of

k (x)

1

, the sum of the roots of

(x - 1) + k (x)

is -

The product of two co-primes is 104. Their L.C.M. should be:

Important Questions on Rational Numbers

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The product of two co-primes is $104$ . Their L.C.M. should be: