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

171.

The H.C.F of 4 × 27 × 3125, 8 × 9 × 25 × 7 and 16 × 81 × 5 × 11 × 49 is = ?

• (A) 180
• (B) 360
• (C) 540
• (D) 1260

Show Answer

 4 × 27 × 3125 = 22 × 33 × 55 8 × 9 × 25 × 7 = 23 × 32 × 52 × 7 16 × 81 × 5 × 11 × 49 = 24 × 34 × 5 × 11 × 72 ∴ H.C.F = 22 × 32 × 5 = 180

172.

A milk vendor has 21 litres of cow milk, 42 litres of toned milk and 63 litres of double toned milk. If he wants to pack them in cans, so that each can contains same litres of milk and does not want to mix any two kinds of milk in a can, then the least number of cans required is = ?

• (A) 3
• (B) 6
• (C) 9
• (D) 12

Show Answer

 For least or minimum number of cans we should have maximum capacity cans for required quantity ⇒ For this we take HCF of given quantities. HCF (21, 42, 63) = 21 ∴ Maximum capacity of a can = 21 litres ∴ Number of cans of cow milk $${\text{ = }}\frac{{21}}{{21}}{\text{ = 1}}$$ ∴ Number of cans of toned milk $${\text{ = }}\frac{{42}}{{21}} = 2$$ ∴ Number of cans of double toned milk $${\text{ = }}\frac{{63}}{{21}} = 3$$ ∴ Total number of cans = 1 + 2 + 3 = 6

173.

Two numbers are in the ratio 3 : 4, if their H.C.F. is 4, then their L.C.M. = ?

• (A) 48
• (B) 42
• (C) 36
• (D) 24

Show Answer

 Let number be = x, y x : y = 3 : 4 (given) H.C.F. = 4 ∴ Number are = x = 4 × 3 = 12 y = 4 × 4 = 16 L.C.M. of (12, 16) = 4 × 3 × 4 = 48

174.

The sum of two numbers is 45. Their difference is $$\frac{1}{9}$$ of their sum. Their LCM is = ?

• (A) 100
• (B) 150
• (C) 200
• (D) 250

Show Answer

 Let the two numbers be a and b Then, a + b = 45.......(i) And a - b = 5......(ii) Adding (i) and (ii) we get 2a = 50 or a = 25 Putting a = 25 in (i) we get b = 20  5   20   -   25      4   -   5  LCM = 5 × 4 × 5 = 100

175.

The HCF and LCM of two 2-digit number are 16 and 480 respectively. The numbers are ?

• (A) 40, 48
• (B) 60, 72
• (C) 64, 80
• (D) 80, 96

Show Answer

 HCF = 16 ∴ Let number are 16x and 16y ⇒ 16xy = 480 ⇒ xy = 30 ∴ Possible pairs = (1, 30), (2, 15), (6, 5) Possible numbers are = (16, 480), (32, 240), (80, 96) ∴ (80, 96) is the answer in the given options of 2 digits.

176.

Reduce $$\frac{128352}{238368}$$  to its lowest terms.

• (A) $$\frac{3}{4}$$
• (B) $$\frac{5}{13}$$
• (C) $$\frac{7}{13}$$
• (D) $$\frac{9}{13}$$

Show Answer

 $$\eqalign{ & {\text{128352}}\overline {)238368{\text{(}}} 1 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{128352}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline {110016{\text{)128352(}}} 1 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,110016 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline {183336{\text{)110016(}}} {\text{6}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{110016}}{ \times } \cr & {\text{So, H}}{\text{.C}}{\text{.F of 128352 and 238368}} \cr & {\text{ = 18336}} \cr & \therefore \frac{{128352}}{{238368}} = \frac{{128352 \div 18336}}{{238368 \div 18336}} = \frac{7}{{13}} \cr} $$

177.

Let x be the smallest number, which when added to 2000 make the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is = ?

• (A) 6
• (B) 5
• (C) 7
• (D) 8

Show Answer

 LCM of 12, 16, 18, 21 = 1008 Next number = 1008 × 2 = 2016 Divisible by all ∴ 16 is added Sum of digits = 1 + 6 = 7

178.

Which greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively ?

• (A) 15
• (B) 30
• (C) 45
• (D) 60

Show Answer

 Required number = HCF if (3026 - 11) and (5053 - 13) HCF of 3015 and 5040 = 45

179.

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

• (A) 15cm
• (B) 25cm
• (C) 35cm
• (D) 42cm

Show Answer

 Required length = HCF of 700cm, 385cm and 1295cm = 35cm

180.

The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case is = ?

• (A) 180
• (B) 176
• (C) 182
• (D) 178

Show Answer

 LCM of 6, 9, 12, 15, 18 is = 180 If 180 is divided by these given number remainder will be 0 ⇒ To leave the same remainder 2 ⇒ The number will be = 180 + 2 = 182