# HCF & LCM

In this section we will be discussing Solved Numerical ability Aptitude Questions and answers on HCF & LCM for GRE, Bank PO, CAT ,competitive Exams and college admission. Few important facts are provided below. MCQ on HCF & LCM are frequently asked in Interviews and Entrance Exams. Regular practice of these problems should help you in good Test score

Here are few quick notes for solving HCF & LCM questions –

• HCF (Highest Common factor) or GCD (Greatest Common Divisor) – The HCF of two or more numbers is the greatest number that divides each of them exactly.
• LCM (Lowest common multiple) – The least number which is exactly divisible by each one of the given numbers is called thier LCM.
• Product of two numbers = Product of their Highest Common factor x Lowest common multiple
• Co-Primes – Two numbers are said to be co-primes if their HCF is 1
• HCF = Highest Common factor of Numerators/ Lowest common multiple of Denominators
• LCM = LCM of Numerators/HCF of Denominators
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Q 1 – The greatest number that divides 204 , 1190 and 1145 exactly is ?
• 13
• 15
• 17
• 19

Q 2 – Find the greatest number that will divide 398,436 and 5427 leaving 7,11 and 15 as reminders respectively ?
• 13
• 15
• 17
• None of the above

Q 3 – Find the greatest number that divides 1541,2443 and 2607 leaving same reminder in each case ?
• 45
• 56
• 67
• 82

Q 4 – The numbers 34041 and 32506 when divided by a certain number of 3 digits leave the same reminder , what is the number ?
• 295
• 307
• 441
• 641

Q 5 – Find the length of the largest possible square slab which can be used in paving the floor 5m 44cm long and 3 m 74 cm broad
• 20 cm
• 26 cm
• 34 cm
• 48 cm

Q 6 – Sum of 2 numbers is 670 and their GCM is 67. How many such pair of numbers are possible ?
• 2 pairs
• 3 pairs
• 4 pairs
• 5 pairs

Q 7 – A trader has 3 kinds of Sugar , of the first kind 117 Kgs, of the second 130 Kgs and of the third kind 143 Kgs. The least number of full casks of equal size in which this can be stored without mixing is ?
• 15
• 20
• 25
• 30

Q 8 – A worker was employed on daily wages for a certain number of days for 495.60. On being absent for some days, he was paid only Rs 389.4. What was his daily wages ?
• 25.25
• 32.40
• 35.40
• 41.75

Q 9 – What is the least number which when divided by 9,12,16,30 leaving in each case, a remainder 3
• 31
• 117
• 231
• 723

Q 10 – Find the smallest number which when increased by 3 is divisible by 21,25,27 and 35 ?
• 3265
• 4722
• 2412
• 2216

Q 11 – Find the least number which when divided by 35 leaves remainder 20, when divided by 45 leaves remainder 30 and when divided by 55 leaves remainder 40 ?
• 2245
• 3125
• 3450
• 4210

Q 12 – Find the least number of four digits which is exactly divisible by 2,3,4,5,6 and 7 ?
• 1260
• 1380
• 1420
• 1480

Q 13 – Five bells toll at intervals of 4,5,7,8 and 10 seconds respectively, beginning together. After what interval of time will they toll again together ?
• 4 minutes 40 seconds
• 5 minutes
• 5 minutes 20 seconds
• 6 minutes

Q 14 – Find the least square number which is exactly divisible by 4,5,6,15 and 18 ?
• 600
• 700
• 800
• 900

Q 15 – Three wheels making 60,36 and 24 revolutions in a minute, start with a certain point in their circumference downwards. They will first come all together again in the same position after how much time ?
• 4 sec
• 5 sec
• 6 sec
• 9 sec