**H.C.F & L.C.M. – Practice Problems**

### Answer : B

### Explanation

L.C.M = 2 x 2 x 2 x 3 x 3 x 5 = 360

Q 2 – The smallest fraction, which each of ^{6}⁄_{7}, ^{5}⁄_{14}, ^{10}⁄_{21} will divide exactly, is?

### Answer : D

### Explanation

Required fraction = L.C.M of^{6}⁄_{7},^{5}⁄_{14},^{10}⁄_{21}=^{L.C.M of 6, 5, 10}⁄_{H.C.F of 7, 14, 21}=^{30}⁄_{7}

Q 3 – The least number, which when divided by 12,15,20 and 54 leaves in each case a remainder of 8, is?

### Answer : B

### Explanation

Required number = (L.C.M of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

Q 4 – 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?

### Answer : A

### Explanation

Let the numbers be a and b. Then a + b = 55 and a x b = 5 x 120 = 600 therefore Required sum =^{1}⁄_{a}+^{1}⁄_{b}=^{a + b}⁄_{a x b}^{55}⁄_{600}=^{11}⁄_{120}

Q 5 – L.C.M of two prime numbers a and b(a>b) is 161. The value of 3b – a is?

### Answer : B

### Explanation

H.C.F of two prime numbers is 1. Product of numbers = (1 x 161) = 161 Let the numbers be a and b. Then a x b = 161 now co-primes with product 161 are (1, 161) (7,23). Since a and b are prime numbers and a > b, we have a = 23 and b = 7. Therefore 3b - a = (3 x 7) - 23 = -2.

Q 6 – The number of prime factors in the expression 2^{5}x2^{6}x3^{6}x5^{3}

### Answer : A

### Explanation

2, 3, 5 are the prime numbers and the given expression is 2^{5}x2^{6}x3^{6}x5^{3}(2^{5}x6^{6}x5^{3}). So the total would be the sum of powers in the expression that is 5+6+6+3=20

### Answer : A

### Explanation

Given numbers are 0.93, 0.60 and 0.75. H.C.F. of 93, 60 & 75 is 3. H.C.F. of given numbers = 0.03

Q 8 – If two numbers are greater than 13 and the H.C.F of two numbers be 13, L.C.M 273, then the sum of the numbers is:

### Answer : B

### Explanation

Let the number be 13 a and 13 b, where a and b are co-primes. Then, 13a * 13b= (13* 273) ⇒ab= 21 Two co-primes with product 21are 3 and 7. ∴ numbers are (13*3, 13*7) i.e , 39 and 91. Their sum = (39+91) = 130

Q 9 – Having two numbers in the ratio 5:7 and their L.C.M as 315, then their product is:

### Answer : A

### Explanation

Let the two numbers be 5x and 7x . Then, their L.C.M is 35 x. 35x = 315 ⇒ x= 9 ∴ The numbers are 45 and 63 and their product is 2835.

Q 10 – If the product of two co-primes is 117 then their L.C.F should be

### Answer : B

### Explanation

H.C.F of co-primes=1 H.C.F * L.C.M = Their product = 117 ∴ 1* L.C.M = 117 ⇒L.C.M = 117