# H.C.F & L.C.M. - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to **H.C.F & L.C.M.**. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using **Show Answer** button. You can use **Next Quiz** button to check new set of questions in the quiz.

### Answer : B

### 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, divisor of 99 are 1, 3, 9, 11, 33, 99 divisor of 101 are 1, 101 divisor of 176 are 1, 2, 4, 8, 16, 22, 44, 88, 176 divisor of 182 are 1, 7, 2, 13, 14, 26, 91, 182 Hence 176 has the most number of divisors.

Q 2 - H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 2^{4} x 3 ^{5} x 5^{2} x 7^{2}?

### Answer : B

### Explanation

3240 = 2^{3}x 3^{2}x 5; 3600 = 2^{4}x 3^{2}5^{2}H.C.F = 36 = 2^{2}x 3^{2}. Since H.C.F is the product of the lowest powers of common factors so the the third number must have 2^{2}x 3^{2}as its factor Since L.C.M is the product of highest powers of common prime factors so the third number must have 3^{5}x 7^{2}as its factor Therefore third number = 2^{2}x 3^{5}x 7^{2}

Q 3 - 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?

### Answer : C

### Explanation

L.C.M of 5,6,7,8 = 840 Therefore Required number is of the form (840k + 3) Least value of k which (840k + 3) is divisible by 9 is k = 2. Therefore Required number = (840 x 2 + 3) = 1683

Q 4 - Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is?

### Answer : D

### Explanation

Let the numbers be 3z, 4z, and 5z. then their L.C.M = 60z So, 60z = 2400 or z = 40. Therefore the numbers are (3 x 40), (4 x 40), (5 x 40). Hence the required H.C.F = 40.

Q 5 - The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and pencils?

### Answer : B

### Explanation

Required number of students = H.C.F of 1001 and 910 = 91.

Q 6 - The least square number which is divisible by 12, 14 and 18 is:

### Answer : A

### Explanation

The least number divisible by12, 14 and 18 is their L.C.M. which is 252. Now 252=2*2*3*3*7 To make it a perfect square, it must be multiplied by 7 2*2*3*3*7*7=1764

### Answer : B

### Explanation

1296=2^{4}x3^{4}and 2400=2^{5}x3x5^{2}HCF=2^{4}x3=48

Q 8 - If the sum of the H.C.F and L.C.F of two numbers is 680 and their L.C.M is 84 times the H.C.F. If one of the numbers is 56, the other number is:

### Answer : D

### Explanation

h+L = 680 and L = 84 h ∴ h+84 h = 680 ⇒ 85h ⇒680 ⇒h= 8 ∴ L= (84*8) = 672 Now, h*L =56*x ⇒ 8* 672= 56*x⇒ x = (8*672)/56 = 96 ∴ The other number is 96.

Q 9 - H.C.F and L.C.F of two numbers x and y are 3 and 105 respectively. If x+y=36 then figure out 1/x + 1/y.

### Answer : D

### Explanation

We have X *y =3 *105 ⇒ xy = 315 ∴ x+y/xy =36/315 = 4/35 ⇒ 1/y+1/x = 4/35 ⇒ 1/x+1/y = 4/35.

Q 10 - Three numbers are in the ratio of 3:4 :5 , their L.C.M is 2400. Their H.C.F is :

### Answer : A

### Explanation

Let the numbers be 3x, 4x and 5x. Then L.C.M = 60x 60x= 2400 ⇒ x= 40 ∴ The numbers are 120, 160 and 200. Clearly , their H.C.F is 40