Mahindra Comviva LCM and HCF Problems with Solutions Quiz- 1

The prime numbers common to given numbers are 2,5 and 7.
H.C.F. = 22x 5 x72 = 980.

108 = 22 x 33, 288 = 25 x 32 and 360 = 23 x 5 x 32.
H.C.F. = 22 x 32 = 36.

1134 ) 1215 ( 1
1134
81 ) 1134 ( 14
81
324
324
x
H.C.F. of 1134 and 1215 is 81.
So, Required H.C.F. = H.C.F. of 513 and 81.
______
81 ) 513 ( 6
__486____
27) 81 ( 3
81
0

H.C.F. of given numbers = 27.

H.C.F. of 391 and 667 is 23.
On dividing the numerator and denominator by 23, we get :
391 = 391 ¸ 23 = 17
667 667¸ 23 29

L.C.M. = Product of highest powers of 2, 3, 5, 7 and 11 = 23 x 33 x 53 x 74 x 11

72 = 23 x 32, 108 = 33x 22, 2100 = 22 x 52 x 3 x 7.
L.C.M. = 23 x 33 x 52x 7 = 37800.

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.
H.C.F. of 0.63, 1.05 and 2.1 is 0.21.
L.C.M. of 63, 105 and 210 is 630.
L.C.M. of 0.63, 1.05 and 2.1 is 6.30.

Let the required numbers be 15.x and llx.
Then, their H.C.F. is x. So, x = 13.
The numbers are (15 x 13 and 11 x 13) i.e., 195 and 143.

Other number = 11 X 693 = 99
77

Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.
495 = 32 x 5 x 11, 900 = 22x 32 x 52, 1665 = 32 x 5 x 37.
H.C.F. = 32 x 5 = 45.
Hence, required length = 45 cm.