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A natural number, when divided by 3, 4, 5, 6, and 7 respectively, leaves corresponding remainder of 2, 3, 4, 5 and 6. What is the smallest of all such numbers fulfilling the above condition ? 
A) 2519
B) 419
C) 209
D) 839
Correct Answer : 419 Explanation : Here 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1, 6 – 5 = 1, 7 – 6 = 1 23, 4, 5, 6, 7 = (2*3*2*5*7) – 1 
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Find the largest five digits number that is divisible by 7, 10, 15, 21 and 25? 
A) 98700
B) 98950
C) 99750
D) None of these
Correct Answer : 99750 Explanation : The least number which is exactly divisible by 7, 10, 15, 21 and 25 is their L.C.M, i.e. 
How many possible pairs of numbers exist whose product is 5400 and HCF is 30? 
A) 1
B) 2
C) 3
D) 4
Correct Answer : 2 Explanation : H.C.F of numbers is 30 So required numbers should be multiple of 30. 
The HCF and LCM of two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is? 
A) 48
B) 36
C) 24
D) 16
Correct Answer : 16 Explanation : lets other number is Z 
Three bells toll at interval of 36 seconds, 40 seconds and 48 seconds respectively. They started ringing together at particular time. They next toll together after? 
A) 12 min
B) 6 min
C) 24 min
D) 18 min
Correct Answer : 12 min Explanation : Least common multiples (LCM) of Interval of bells toll: 
Three wheels can complete 60, 36, 24 revolutions per minute respectively. There is red mark on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again? 
A) 2.5 second
B) 1.6 second
C) 5 second
D) 7.5 second
Correct Answer : 5 second Explanation : The first wheel spins at 60 rpm which means that it completes 60/60 = 1 revolution every second. 
Find the HCF of the numbers a and b, where a = 25*32*76*114 and b = 23*34*56*11*133 ? 
A) 396
B) 408
C) 792
D) 1584
Correct Answer : 792 Explanation : HCF is the product of all common prime factors using the least power of each common prime factor 

What is the least number of that is exactly divisible by 4, 12, 15, and 18? 
A) 120
B) 108
C) 180
D) 240
Correct Answer : 180 Explanation : The least number which is exactly divisible by is their LCM of (4, 12, 15, and 18) 
The HCF of 2 numbers is 11 and LCM is 693.If one of numbers is 77.find the other number ? 
A) 99
B) 198
C) 66
D) 143
Correct Answer : 99 Explanation : Product of two numbers = Product of their HCF and LCM 
The largest number , which exactly divides 210, 315, 147 and 168 is ? 
A) 3
B) 7
C) 21
D) 4410
Correct Answer : 21 Explanation : The largest number is the H.C.F. of 210, 315, 147, and 168, which is 21. 

The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is ? 
A) 33
B) 66
C) 132
D) 264
Correct Answer : 132 Explanation : Product of two numbers = Product of their HCF and LCM. First number = 2 x 44 = 88 
Find the HCF of 2^{2} * 3^{2}, 2 * 3^{4} * 7 ? 
A) 128
B) 126
C) 146
D) 434
Correct Answer : 126 Explanation : 2^{2} * 3^{2} =>2*2*3*3 HCF is the product of all common prime factors using the least power of each common prime factor. 
Find the HCF of 54, 288 and 360 ? 
A) 18
B) 36
C) 54
D) 72
Correct Answer : 18 Explanation : Let’s solve this question by factorization method. 
PQRS is the greatest number of 4 digits which when divided by any of the numbers 6, 9, 12 or 17 leaves a remainder of 2 in each case. What is the value of (P + R)/(Q + S)? 
A) 18
B) 18/11
C) 11/18
D) 9/11
Correct Answer : 18/11 Explanation : The required number, which is exactly divisible by each one of the given numbers, should be divisible by LCM of (6, 9, 12, 17) i.e. 612 But we should get the remainder as 2,so we need to add 2 to 9792.So the number PQRS is 9794. Thus, required value (P + R)/(Q + S) = (9+9)/(7+4) 
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ? 
A) 7
B) 8
C) 9
D) 11
Correct Answer : 8 Explanation : L.C.M. of 6, 5, 7, 10 and 12 is 420. So, the bells will toll together after every 420 seconds i.e. 7 minutes. Now, 7 x 8 = 56 and 7 x 9 = 63. Thus, in 1hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start. 
The sum and difference between LCM and HCF of two numbers is 84 and 60 respectively. If one of the numbers is 24, find the other number? 
A) 48
B) 36
C) 54
D) 16
Correct Answer : 36 Explanation : As given, When add eq1 and 2 then LCM × HCF = Ist number ×IInd number Or Product of numbers = HCF × LCM 
The LCM and HCF of two numbers are 240 and 16 respectively. If the two numbers are in the ratio 3 : 5, the numbers are ? 
A) 24,40
B) 21,35
C) 36,60
D) 48,80
Correct Answer : 48,80 Explanation : Suppose two numbers are 3x and 5x. 