L.C.M and H.C.F : Aptitude Test

  • 1. The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is: 
A.) 544
B.) 548
C.) 504
D.) 536

Answer: Option 'B'

Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.

  • 2. Find the highest common factor of 36 and 84.
A.) 4
B.) 6
C.) 12
D.) 18

Answer: Option 'C'

36 = 22 x 32
84 = 22 x 3 x 7
H.C.F. = 22 x 3 = 12.

  • 3. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is: 
A.) 85
B.) 75
C.) 65
D.) 60

Answer: Option 'A'

Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
First number = 551/29 = 19; Third number = 1073/29 = 37.
Required sum = (19 + 29 + 37) = 85.

  • 4. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
A.) 15 cm
B.) 35 cm
C.) 25 cm
D.) 52 cm

Answer: Option 'B'

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

  • 5. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:
A.) 127
B.) 305
C.) 235
D.) 123

Answer: Option 'A'

Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.