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Aptitude HCF AND LCM Practice QA-Easy

2929.The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
1008
1015
1022
1032
Explanation:

Required number = L.C.M. of $\left(12,16, 18, 21, 28\right)$ + 7

   = 1008 + 7

   = 1015

2930.Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
4
10
15
16
Explanation:

L.C.M. of 2, 4, 6, 8, 10, 12 is 120.

So, the bells will toll together after every 120 seconds [2 minutes].

In 30 minutes, they will toll together$ \dfrac{30}{2} $+ 1 = 16 times.

2932.252 can be expressed as a product of primes as:
2 x 2 x 3 x 3 x 7
2 x 2 x 2 x 3 x 7
3 x 3 x 3 x 3 x 7
2 x 3 x 3 x 3 x 7
Explanation:
Clearly, 252 = 2 x 2 x 3 x 3 x 7.
2933.The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
123
127
235
305
Explanation:

Required number = H.C.F. of $\left(1657 - 6\right)$ and $\left(2037 - 5\right)$

  = H.C.F. of 1651 and 2032 = 127.

2934.Find the highest common factor of 36 and 84.
4
6
12
18
Explanation:

36 = 22 x 32

84 = 22 x 3 x 7

$\therefore$ H.C.F. = 22 x 3 = 12.

2935.What is the smallest number which when diminished by 12, is divisible 8, 12, 22 and 24?
276
264
272
268
Explanation:

Required Number

= LCM of [8, 12, 22 and 24] + 12

= 264 + 12 = 276

2937.The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
276
299
322
345
Explanation:

Clearly, the numbers are $\left(23 \times 13\right)$ and $\left(23 \times 14\right)$.

$\therefore$ Larger number = $\left(23 \times 14\right)$ = 322.

2938.504 can be expressed as a product of primes as
2 × 2 × 3 × 3 × 7 × 7
2 × 3 × 3 × 3 × 7 × 7
2 × 3 × 3 × 3 × 3 × 7
2 × 2 × 2 × 3 × 3 × 7
Explanation:

It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7

2940.The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
28
32
40
64
Explanation:

Let the numbers be 2 x and 3 x .

Then, their L.C.M. = 6 x .

So, 6 x = 48 or x = 8.

$\therefore$ The numbers are 16 and 24.

Hence, required sum = $\left(16 + 24\right)$ = 40.

2941.What is the HCF of 1/3,2/3, and 1/4 ?
2/3
1/3
1/4
1/12
Explanation:

HCF of fractions = $\dfrac{\text{HCF of Numerators}}{\text{LCM of Denominators}}$

HCF of $\dfrac{1}{3}$ , $\dfrac{2}{3}$ and $\dfrac{1}{4}$

$=\dfrac{\text{HCF (1, 2, 1)}}{\text{LCM (3, 3, 4)}}$

$=\dfrac{1}{12}$

2960.The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, then the other is:
30
28
24
20
Explanation:

Product of two numbers = Product of their HCF and LCM.

Let one number $=x$

=> $25 \times x = 5 \times 150$

=> $x=\dfrac{5 \times 150}{25}=30$

2961.What is the greatest possible length which can be used to measure exactly the lengths 8 m, 4 m 20 cm and 12 m 20 cm?
10 cm
30 cm
25 cm
20 cm
Explanation:

Required length

= HCF of 800 cm, 420 cm, 1220 cm

= 20 cm

2962.The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
504
536
544
548
Explanation:

Required number = L.C.M. of $\left(12, 15, 20, 54\right)$ + 8

   = 540 + 8

   = 548.

2963.The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
15 cm
25 cm
35 cm
42 cm
Explanation:

Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

2964.What is the greatest number which on dividing 1223 and 2351 leaves remainders 90 and 85 respectively?
1133
127
42
1100
Explanation:

Required number
= HCF of $\left(1223 - 90\right)$ and $\left(2351 - 85\right)$
= HCF of 1133 and 2266
= 1133

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