Tag: hcf-lcm

Questions Related to hcf-lcm

What is the greatest possible rate at which a man can walk 68 km, 102 km and 51 km in exact number of days?

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. 17

  2. 4

  3. 7

  4. 3

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Correct Option: A
Explanation:

Required rate = H.C.F. of (68 km, 102 km, 51 km) = 17 km per day

The HCF of $136, 170$ and $255$ is

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $13$

  2. $15$

  3. $17$

  4. $1$

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Correct Option: C

Find the greatest number which divides 120, 165 and 210 exactly leaving remainders 5, 4 and 3 respectively

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. 7

  2. 5

  3. 23

  4. None of these

Show answer
Correct Option: D
Explanation:

The required number will be the H.C.F of (120 - 5), (165 - 4) and (210 - 3) i.e. H.C.F. of 115
161 and 207
$\displaystyle \therefore $ Required number = H.C.F. of 115, 161 and 207 = 23

HCF of $24, 36$ and $92$ is:

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $24$

  2. $36$

  3. $12$

  4. $4$

Show answer
Correct Option: D
Explanation:

The HCF of $24,36,92$ can be found by factorising all three numbers:

$24= 2 \times 2 \times 2 \times 3 $
$36= 2 \times 2 \times 3 \times 3 $
$92 =2 \times 2 \times 23 $
Now, common factors are $2$ and $2$
So, HCF is $ 2 \times 2=4$
Hence, the answer is $4$.

The HCF of $18$ and $30$ is equal to

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $6$

  2. $5$

  3. $4$

  4. $3$

Show answer
Correct Option: A
Explanation:

$18 = 2 \times 3 \times 3$

$30 = 2 \times 3 \times 5$
So, H.C.F of $18$ and $30$ is $6$.
So, option A is correct.

The HCF of $75$ and $15$ is equal to

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $12$

  2. $13$

  3. $14$

  4. $15$

Show answer
Correct Option: D
Explanation:

$75=5^2\times 3$

$15=5\times3$
HCF$=15$

What is the least number by which $825$ must be multiplied in order to produce a multiple of $715 ?$

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $13$

  2. $15$

  3. $11$

  4. $3$

Show answer
Correct Option: A
Explanation:

$825=3\times5\times5\times 11$

$715=5\times11\times13$
In the factor of both numbers, $13$ is not common. 
Hence, the least number by which $825$ must be multiplied in order to produce a multiple of $715=13.$

The the H.C.F of $420$ and $396$ is equal to

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $12$

  2. $13$

  3. $14$

  4. $15$

Show answer
Correct Option: A
Explanation:

$420 =7 \times 5\times 3\times 2^2$
$396=2^2 \times 3^2\times 11$
So, $H.C.F=2^2 \times 3$
Ans- Option $A$

The HCF of $12$ and $24$ is equal to

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $6$

  2. $12$

  3. $24$

  4. None of the above

Show answer
Correct Option: B
Explanation:

$12 = 2 \times 2 \times 3 $

$24 = 2 \times 2 \times 2 \times 3$ 
So, HCF of $12$ and $24$ is $12$.
So, option B is correct.

The HCF of $75$ and $180$ is equal to

maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

  1. $11$

  2. $12$

  3. $13$

  4. $15$

Show answer
Correct Option: D
Explanation:
$180=60 \times 3 =5\times2^2\times 3^2$
$75=5^2 \times 3$
HCF$=15$