# H.C.F and L.C.M Problems Question & Answers

### The greatest possible length which can be used to measure exactly the length 7m, 3m 85cm, 12 m 95 cm is

 A) 15 cm B) 25 cm C) 35 cm D) 42 cm
Answer & Explanation Answer: C) 35 cm

Explanation:

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

‹=› 35 cm.

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Submitted By: Raju
Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

### The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

 A) 1677 B) 1683 C) 2523 D) 3363
Answer & Explanation Answer: B) 1683

Explanation:

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

${\color{Blue}&space;\therefore&space;}$ Required number is of the form 840k + 3

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

${\color{Blue}&space;\therefore&space;}$ Required number = (840 x 2 + 3) = 1683.

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Submitted By: madhu9669
Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

### If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:

 A) 55/601 B) 601/55 C) 11/120 D) 120/11
Answer & Explanation Answer: C) 11/120

Explanation:

Let the numbers be a and b.

Then, a + b = 55 and ab = 5 x 120 = 600.

${\color{Blue}&space;\therefore&space;}$ The required sum =(1/a)+(1/b)=(a+b)/ab=55/600=11/120

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Submitted By: madhu9669
Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

### Which of the following has the most number of divisors?

 A) 99 B) 101 C) 176 D) 182
Answer & Explanation Answer: C) 176

Explanation:

99 = 1 x 3 x 3 x 11

101 = 1 x 101

176 = 1 x 2 x 2 x 2 x 2 x 11

182 = 1 x 2 x 7 x 13

So, divisors of 99 are 1, 3, 9, 11, 33, .99

Divisors of 101 are 1 and 101

Divisors of 176 are 1, 2, 4, 8, 11, 16, 22, 44, 88 and 176

Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182.

Hence, 176 has the most number of divisors.

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Submitted By: madhu9669
Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability

### The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is:

 A) 123 B) 127 C) 235 D) 305
Answer & Explanation Answer: B) 127

Explanation:

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

= H.C.F. of 1651 and 2032 = 127.

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Submitted By: madhu9669
Subject: H.C.F and L.C.M Problems - Quantitative Aptitude - Arithmetic Ability