First Naukri HCF and LCM Quiz -1

Solution:

Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.

Without decimal places, these numbers are 63, 105 and 210.

Now, H.C.F of 63, 105 and 210 is 21.

Therefore,  H.C.F, of 0.63, 1.05 and 2.1 is 0.21.

L.C.M. 63, 105 and 210 is 630

Therefore,  L.C.M. of 0.63, 1.05 and 2.1 is 6.30.

Solution:

3    |    6 - 7 - 8 - 9 - 12

2    |    2 - 7 - 8 - 3 -  4

2    |    1 - 7 - 4 - 3 -  2

|    1 - 7 - 2 - 3 -  1

Therefore,     L.C.M. = 3 \times 2 \times 2 \times 7 \times 2 \times 3 = 504

Hence, required number = (504 + 1) = 505.

Solution:

Required number  = H.C.F. of (132 – 62), (237 – 132) and (237 –  62)

= H.C.F. = 70, 105 and 175 = 35.

Solution:

L.C.M. of 5, 6, 7, 8 = 840.

The required number is of form 840k + 3.

The least value of k for which (840k + 3) is divisible by 9 is k = 2.

Therefore, Required number = (840 \times 2 + 3) = 1683

Solution:

Required length = H.C.F. of 495 cm, 900 cm, and 1665 cm.

495 = 3^{2} × 5  × 11,  900 = 2^{2} × 3^{2} × 5^{2},   1665 = 3^{2} × 5 × 37

H.C.F. = 3^{2} × 5 = 45

Hence, required length = 45cm.

Solution:

Required number = L.C.M of 12, 15, 20, 27.

3    |    12 - 15 - 20 - 27

4    |      4 -  5  - 20 -  9

5    |      1 -  5  -  5  -  9

|      1 -  1  -  1  -  9

Therefore,  L.C.M  = 3 \times 4 \times 5 \times 9 = 540

Hence, the required number is 540.

Solution:

Required number = H.C.F of (1657 - 6) and (2037 - 5) = H.C.F of 1651 and 2032.
1651 ) 2032 ( 1
1651
381 ) 1651 ( 4
1524
127)381 ( 3
381
---------
xxxxx
Therefore, the Required number = 127.

Solution:

The largest number of four digits is 9999.

The required number must be divisible by L.C.M of 12, 15, 18, 27 i.e, 540.

On dividing 9999 by 540, we get 279 as the remainder.

∴  Required number = (9999 - 279) = 9720.

H.C.F of given fractions =  (H.C.F of 2, 8, 16, 10)/(L.C.M of 3, 9, 81, 27) = 2/81.

L.C.M of the given fractions =  (L.C.M of 2, 8, 16, 10)/(H.C.F of 3, 9, 81, 27) = 80/3

Solution:

HCF of (80 -34 ), (153 – 80), (153-34)

HCF 46, 73, and 119

The factors of 46 are: 1, 2, 23, 46

The factors of 73 are: 1, 73

The factors of 119 are: 1, 7, 17, 119

Then the greatest common factor is 1.