X = 12 (Factor 1,2,3,4,6,12)
Y = 24 (Factor = 1,2,3,4,6,8,12,24)
Smallest x+y = 12+24 = 36

Thank for sharing a
But how about using lcm answer this question ? Teacher do not allow this method.

LCM method :


X has factors 3, 4, 6

3 = 3¹

4 = 2 × 2 = 2²

6 = 2 × 3 = 2¹ × 3¹


LCM of these three numbers

= 2² × 3¹
= 4 × 3
= 12


Likewise,

Y has factors 4, 8, 12

4 = 2 × 2 = 2²

8 = 2 × 2 × 2 = 2³

12 = 2 × 2 × 3 = 2² × 3¹


LCM of these three numbers

= 2³ × 3¹
= 8 × 3
= 24



Smallest possible X + Y

= 12 + 24
= 36

P6 learned LCM ? Sec 1 standard :)

This one is primary school Olympiad question so I guess they learnt many things ahead.

OK.
And this method involved prime factor too.

Ya it is math olympiad question. Wow this is secondary question

May I ask. Why factor of 12 , can 2x2x3 to mix together ?

What is meant by mix together?

Product of prime numbers.
Divide 12 all the way till get 1
12÷②=6
6÷② =3
3÷③ = 1
Therefore, 12= ②×②×③

Think you refer to how to get LCM = 12?

Ya. I don't know how lcm 12 but now I know how it's works. But if any other number other than 12. Example 13 or 14 or 15 also can use this method to reduce to 1 is it ?

Yes. This is known as prime factorisation.


Divide the number by the smallest prime factor 2 first . If divisible, continue dividing by 2 If not divisible, go to the next prime factor , 3.

If divisible, continue dividing by 3. If not, go to the next prime factor 5. And so on.

Repeat this and keep going up until you finally divided the number completely to reach 1.


Prime numbers are numbers that are exactly divisible by themselves or 1 only.
(1 is not considered prime)


The first few are 2,3,5,7,11,13,17,19...

The idea of LCM is to first break each number into a product of their prime factors.

Prime factors are the simplest and cannot be divided anymore except by themselves or by 1.


Then, we look at the numbers' prime factors and among the same ones, pick the ones with the highest power.

eg. We picked the 2² for the earlier example and 3¹.

Also, if a prime factor only appears in one number, we pick it as well.

These ensures that the multiple we get is divisible by all the numbers. (And that's why it's called a common multiple).

We don't pick extra copies of the prime factors (that's why we don't have 2 x 2 x 2 for the LCM of 12) so that we can get the lowest common multiple.

Picking the highest power of each prime factor is sufficient to get the common multiple.

Oooohh I see. Okok . Now I know. Thank you so much . For your patience and help. At least I'm not so blur now. Thank you so much. So kind of you guys .

Still sound hard for me but I will try my best of understanding it. Thank you for your kind help.