Number System

The answer is 1 greater than Least Common Multiple of 3, 4 and 5 which, when divided by them shall yield 1 as remainder. The LCM of 3, 4 & 5 is 60.

Therefore correct answer is 61.

Correct.The answer is the number which is 7 more than the LCM of the three given numbers.

Hence, correct answer is 600 + 7 = 607.

Correct.

For the two numbers, their Product = LCM x HCF.

Therefore, HCF = (Product of two numbers) / (LCM) 

i.e.  HCF = 1260 / 210 = 6

Required number = HCF of (251 - 1), (326 - 6) and (194 - 2) 

= HCF of 250, 320 and 192

= 64

So, the required number is 64.

Let the smallest 3-digit number be 1000.

Now, LCM of 8, 16, 24 and 36 = 144

On dividing 1000 by 144,

Dividend = quotient x divisor + remainder

1000 = 6 x 144 + 136

So, the required number is = 1000 + (144 - 136) + 11 = 1000 + 8 + 11 = 1019.

Let the numbers be 21a and 21b.

So, 21a - 21b = 63

a - b = 3

So, 4 - 1 = 3

So, the numbers are 84 (4 x 21) and 21 (1 x 21).

65 - 51 = 14, 55 - 41 = 14 and 45 - 31 = 14

Therefore, required number = (LCM of 65, 55 and 45) - 14

= 6435 - 14

= 6421 

So, the required number is 6421.

LCM of 35, 14 and 21 = 210

Now, multiple of 210 which lies between 200 and 400 is 210 x 1 = 210.

So, required number = 210 + 5 = 215

If the division of 96 by m leaves the remainder 5, then 91 must be divisible by m without remainder.  Similarly, if the division of 120 by m leaves the remainder 3, then 117 must be divisible by m without  remainder. So, m must be a divisor of both 91 and 117. Among the choices, it is only 13 which satisfies this  condition.

First, find the least 2 digit number which gives remainder 4. That number is 11. So, the equation is like 7(x) + 4, where x = 4...13. x cant be greater than 13 as the highest 2 digit number is 95. So, sum = 7(1 + 2 + ... + 13) + 4.13 = 689, using AP series. So, option 3 is correct.

9 & 10 are both composite numbers and their HCF is 1. Hence, this option is correct.

[ Explanation: Product of numbers= HCF x LCM 2160= 12 x LCM LCM= 2160/12= 180]

HCF X LCM = product of two numbers

The last four number divide by 16. 2460/16 leaves a remainder of 12.

hcf of(127-55),(175-127)(175-55)