Practice MCQ Questions and Answer on Problems on H.C.F and L.C.M

151.

A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?

• (A) 26 minutes and 18 seconds
• (B) 42 minutes and 36 seconds
• (C) 45 minutes
• (D) 46 minutes and 12 seconds

Show Answer

 L.C.M. of 252, 308 and 198 = 2772 So, A, B and C will again meet at the starting point in 2772 sec. i.e., 46 min. 12 sec.

152.

The LCM of three different numbers is 120. Which of the following cannot be their HCF ?

• (A) 8
• (B) 12
• (C) 24
• (D) 35

Show Answer

 Since HCF is always a factor of LCM, we cannot have three numbers with HCF 35 and LCM 120.

153.

The simplest reduction to the lowest terms of $$\frac{{116690151}}{{427863887}}$$   is = ?

• (A) $$\frac{{3}}{{11}}$$
• (B) $$\frac{{7}}{{11}}$$
• (C) $$\frac{{11}}{{3}}$$
• (D) None of these

Show Answer

 $$\eqalign{ & {\text{116690151}}\overline {){\text{427863887(}}} {\text{3}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{350070453}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline {{\text{77793434)116690151(}}} 1 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{77793434}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline {{\text{38896717)77793434(}}} {\text{2}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{77793434}}{ \times } \cr & {\text{So, H}}{\text{.C}}{\text{.F of 116690151 and 427863887}} \cr & {\text{ = 38896717}} \cr & \therefore \frac{{116690151}}{{427863887}} = \frac{{116690151 \div 38896717}}{{427863887 \div 38896717}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{3}{{11}} \cr} $$

154.

The greatest number which when divides 989 and 1327 leave remainder 5 and 7 respectively = ?

• (A) 8
• (B) 16
• (C) 24
• (D) 32

Show Answer

 989 - 5 = 984 1327 - 7 = 1320 Subtract the remainder from the number. HCF = (984, 1320) = 24 for greatest number take HCF of the numbers.

155.

The difference between the greatest and least prime numbers which are less then 100 is = ?

• (A) 95
• (B) 96
• (C) 97
• (D) 94

Show Answer

 Greatest prime number = 97 Least prime number = 2 So, their difference 97 - 2 = 95

156.

Find the smallest 5-digit number which when divided by 15, 20 and 25 leaves remainders 7, 12 and 17, respectively.

• (A) 10195
• (B) 10192
• (C) 10193
• (D) 10194

Show Answer

 Five-digit smallest number = 10000 Five-digit system number which is exactly divisible by 20, 25, 15 and leaves remainder 12, 17, 7 - means gap = 20 - 12 = 25 - 17 = 15 - 7 = 8 ⇒ 10000 + 200 - 8 = 10192 Answer

157.

If three number are 2a, 5a and 7a, what will be their LCM ?

• (A) 70a
• (B) 65a
• (C) 75a
• (D) 73a

Show Answer

 The given three numbers are 2a, 5a and 7a LCM of 2a, 5a and 7a = 2 × 5 × 7 × a = 70a

158.

A general of an Army wants to create a formation of square from 36562 army men. After arrangement, he found some army men remainder unused.

• (A) 36
• (B) 65
• (C) 81
• (D) 97

Show Answer

 So, after making 191 group of square 81 Men will be left.

159.

The least number which when increased by 5 is divisible by each one of 24, 32, 36 and 54 is = ?

• (A) 427
• (B) 859
• (C) 869
• (D) 4320

Show Answer

 = (LCM of 24, 32, 36, 54) - 5 = 864 - 5 = 859

160.

The G.C.D. (greatest common divisor) of 1.08, 0.36, 0.9 is = ?

• (A) 0.03
• (B) 0.9
• (C) 0.18
• (D) 0.108

Show Answer

 Given numbers are 1.08, 0.36 and 0.90 HCF of 108, 36 and 90 is 18 ∴ HCF of given numbers = 0.18