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

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.

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.

24=2*2*2*3 ///24=2*3*4 not possible **use small numbers **.
36=2*2*3*3.
40=2*2*2*5.

Now take common from combination of 3 numbers i.e 2,2.
Now take common from combination of 2 numbers i.e 2,3.

Now use numbers which do not have pair i.e 3,5.

Now multiply 2*2*2*3*3*5=360.

Ans is 360.

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.

@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.

If we do the LCM process with 6, 4, 2 as divisors we are getting the LCM as 720 and with the numbers 2, 2, 3, 2 as divisors we are getting 360 as LCM.

Why that difference is occurring and which one we should consider as LCM?

@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.

Better method:

LCM (24,36,40) = LCM (4*6,4*9,4*10).
LCM(6,9,10) = 90 //Can be easily calculated.

So, LCM of (24,36,40) = 4 * 90 = 360 // 4 was the common factor so it is multiplied now.

24 = 2*2*2*3.
36 = 2*2*3*3.
40 = 2*2*2*5.

For 24 = 2*3*4. We can not take 4 because 4 is not prime no.

Same applies for 40 = 2x4x5. 4 is not prime so don't take it use 40 = 2x2x2x5.

We generally break the numbers into prime numbers.

So if 24 = 2*12 = 2*(3*4) = 2*3*2*2 = 2^3*3.

Follow this for the other numbers too. This is the shortcut and safest method.