Aptitude - Problems on H.C.F and L.C.M - Discussion

@All.

Among 24, 36, 40.
36 is divisible by 9.
So, our answer is also divisible by 9.
In the given options, only 360 is divisible by 9.
So, that's the answer.

@All.

Get large element:
And then(large element/common number)× second largest element.

24, 36 ,40
Large = 40.
Common number that divide all three =4
(40/4) = 10
Second large = 36 × 10 =360.

@All.

Here, You just need to find the prime factors of each number.

24 = 2^3 * 3.
36 = 2^2 * 3^2.
40 = 2^3 * 5.
Now take each prime factor with its highest power and multiply them.
i.e. , 2^3 *3^2 * 5 = 8 * 9 * 5 = 360.
L. C. M. Of 24, 36, 40 is 360.

2 |24 36 40
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2|12 18 20
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2|6 9 10
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3 |3 9 5
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3 |1 3 5
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5| 1 1 5
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1 1 1

2 * 2 * 2 * 3 * 3 * 5 = 360.

One of the methods you can try is :
24, 36, 40

Take the largest num: 40. Check whether 40 is completely divisible by rest. If it is then that number will be the lcm.

If not: take the twice of largest (40*2=80)
And check whether 80 will get completely divisible.
If not take thrice and go on till we get the number.

For eg:
4,12 = lcm is 12.
6, 3, 18 = lcm is 18.
10, 15 = lcm is 30(largest number =15 ; but 15 is not divisible by 10. So take the twice 15*2=30. 30 will be divisible by 10 n 15 .. So 30 is the answer).

Try with more examples.

In the given options 120, 240, 360, 480.

Only 360 is divisible by all nos i.e. 24, 36, 40.

Nice explanation, thankyou @Tripura.

We can use digital sum method.

i.e if one of the numbers of the given set has the sum with 9 given numbers 2+4=6;3+6=9;4+0=4.then the answer will also contain a digital sum as 9.

a) 1+2+0=3
b) 2+4+0=6
c) 3+6+0=9
d) 4+8+0=12.

So, the answer is 360 which contains 9 as its sum.

Thanks for all your solution.

Guys, 360 is the correct answer.

And the answer given is the simplest answer if you know how to do it.