বিগত সালের প্রশ্ন ও প্রশ্ন ব্যাংক
বিসিএস, ব্যাংক, প্রাথমিক শিক্ষক ও সকল সরকারি চাকরির বিগত সালের প্রশ্ন ও অধ্যায়ভিত্তিক নির্ভুল সমাধান
Let,
these two numbers be 3x and 4x
then their LCM = 12x
Now,
according to question,
12x = 240
Or, x = 20
Thus,
the numbers are (3x = 3 × 20) = 60 and (4x = 4 × 20) = 80
Then smaller in this two is 60
In this type of problem we find the difference of divisors and their remainders.
Here difference,
32 - 10 = 22
40 - 18 = 22
72 - 50 = 22
Here, in each case difference is same i.e. 22
Then required number of pebbles is given by [(LCM of 32, 40, 72) -22]
32 = 2 × 2 × 2 × 2 × 2
40 = 2 × 2 × 2 × 5
72 = 2 × 2 × 2 × 3 × 3
Hence,
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440
Thus, Required number of pebbles, = 1440 - 22 = 1418
We have to find the Least number, therefore we find out the LCM of 8, 12, 16 and 20.
8 = 2 × 2 × 2;
12 = 2 × 2 × 3;
16 = 2 × 2 × 2 × 2;
20 = 2 × 2 × 5;
LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240;
This is the least number which is exactly divisible by 8, 12, 16 and 20
Thus,
Required number which leaves remainder 5 is, 240 + 5 = 245
In this type of question, We need to find out the LCM of the given numbers. LCM of 12, 15, 18 and 20; 12=2×2×3;
15=3×5;
18=2×3×3;
20=2×2×5;
Hence, LCM = 2×2×3×5×3 Since, the soldiers are in the form of a solid square. Hence, LCM must be a perfect square.
To make the LCM a perfect square, We have to multiply it by 5,
hence,
The required number of soldiers = 2×2×3×3×5×5 = 900
Let the numbers be x, 2x and 3x.
The HCF in x, 2x and 3x is x because 1, 2, 3 are prime.
Hence, x = 12; then the other numbers are 24 and 36.