LCM and HCF

LCM and HCF

Easy Questions
Moderate Questions
Difficult Questions
LCM and HCF Tutorial

Aptitude

Simplification
Number System
Fractions
Elementary Algebra
LCM and HCF
Approximation
Unitary Method
Linear Equation
Quadratic Equation
Discount
Average
Surds and Indices
Percentage
Square root and cube root
Order of Magnitude
Work and Wages
Odd Man Out and Series
Algebra
Profit and Loss
Stocks and Shares
True Discount
Ratio, Proportion
Partnership
Alligation or Mixture
Time and Work
Pipes and Cistern
Speed, Time and Distance
Problem on Trains
Height and Distance
Banker's Discount
Boats and Streams
Races and games
Problems on Ages
Clocks and Calendars
Simple interest
Compound Interest
Sets and Functions
Area and Perimeter
Volume and Surface Area of Solid Figures
Sequences and Series
Plane Geometry
Logarithm
Probability
Permutation and Combination
Statistics
Mensuration
Trigonometry
Aptitude miscellaneous
  1. Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time ?








  1. View Hint View Answer Discuss in Forum

    Required time = LCM of 200, 300, 360 and 450 seconds
    We find , LCM of 200, 300, 360 and 450 seconds = 1800 seconds

    Correct Option: A

    Required time = LCM of 200, 300, 360 and 450 seconds
    We find , LCM of 200, 300, 360 and 450 seconds = 1800 seconds
    ∴ Required time = 1800 seconds

  1. From a point on a circular track 5 km long A, B and C started running in the same direction at the same time with speed of 21/2 km per hour, 3 km per hour and 2 km per hour respectively. Then on the starting point all three will meet again after








  1. View Hint View Answer Discuss in Forum

    A makes one complete round of the circular track in

    5
    		= 2 hours,
    5
    2

    B in
    5
    		hours and C in
    5
    		hours.
    32

    That is after 2 hours A is at the starting point,
    B after
    5
    		hours and C after
    5
    		hours.
    32

    Hence the required time = LCM of 2,
    5
    		and
    5
    		hours
    32

    Required time =
    LCM of 2, 5, 5
    HCF of 1 , 3 , 2

    Correct Option: C

    A makes one complete round of the circular track in

    5
    		= 2 hours,
    5
    2

    B in
    5
    		hours and C in
    5
    		hours.
    32

    That is after 2 hours A is at the starting point,
    B after
    5
    		hours and C after
    5
    		hours.
    32

    Hence the required time = LCM of 2,
    5
    		and
    5
    		hours
    32

    Required time =
    LCM of 2, 5, 5
    HCF of 1 , 3 , 2

    Required time =
    10
    		 = 10 hours.
    1

  1. The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10 : 15 : 00 AM, then at what time will they again change simultaneously?








  1. View Hint View Answer Discuss in Forum

    LCM of 24, 36 and 54 seconds = 216 seconds = 3 minutes 36 seconds
    ∴ Required time = 10 : 15 : 00 +
    3 minutes 36 seconds

    Correct Option: B

    LCM of 24, 36 and 54 seconds = 216 seconds = 3 minutes 36 seconds
    ∴ Required time = 10 : 15 : 00 +
    3 minutes 36 seconds
    Hence , Required time = 10 : 18 : 36 a.m.

  1. Four bells ring at intervals of 4, 6, 8 and 14 seconds. They start ringing simultaneously at 12.00 O’clock. At what time will they again ring simultaneously ?








  1. View Hint View Answer Discuss in Forum

    LCM of 4, 6, 8, 14 = 168 seconds = 2 minutes 48 seconds
    They ring again at 12 + 2 min. 48 sec.

    Correct Option: A

    LCM of 4, 6, 8, 14 = 168 seconds = 2 minutes 48 seconds
    They ring again at 12 + 2 min. 48 sec.
    Required time = 12 hrs. 2 min. 48 sec.

  1. When a number is divided by 15, 20 or 35, each time the remainder is 8. Then the smallest number is








  1. View Hint View Answer Discuss in Forum

    As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
    LCM of 15, 20 and 35 ( k ) = 420
    Here , remainder = 8

    Correct Option: A

    As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
    LCM of 15, 20 and 35 ( k ) = 420
    Here , remainder = 8
    ∴ Required least number = 420 + 8 = 428