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

By formula;.

Given reminder is 4, and divisor is 6, 9, 15, 18 and lcm of 6, 9, 15, 18 is 90. To find dividend we have to multiply 90 with remainder 4 and then add remainder ie 4.

You don't need to take anything on right-hand side. Just see whether the values of k when multiplied and added are a multiple of 7.

Hey guys, what will we take in the right-hand side? Please help me out.

90k + 4/7 find k.
90k/7 + 4/7.

We have to distribute 90 k as multiple of 7 and divisible by 7.
12 * 7k + 6k + 4/7.
12 * 7k/7 + 6k + 4/7.

Now we can put the value of k in 6k+4/7.

@Priya it is so easy.

6 = 2 * 3
9 = 3 * 3
15 = 3 * 5
18 = 2 * 3 * 3.

Take one number from common multiple and multiply rest digits.
2*3*3*5.

How Lcm of 90 come? Please explain.

I understand you trick, Thank you @Jignesh Rajput.

Guys , here it is asked the least multiple so the answer is 94.

This will satisfy all the conditions.

Hi, friends it's very simple trick.

LCM of 6, 9, 15, 18 is 90.

We can simply write the answer 90 + 4 but in question, it should be multiple of 7.

So (90k + 4) / 7 now we have to find the value of 'k' to complete the answer.

The first method is to substitute the value of k = 1, 2, 3. And divide it by 7 and sees the result. It actually time taking.

Now the trick:

(90k + 4) / 7 = 90k / 7 + 4 / 7,

The remainder of 4 / 7 is 4,

Remainder 90k / 7 is 6k.

Now add both remainders 6k+4 it should be divided by 7.

Now substitute the value of k it comes out be 4.

Put 90 * 4 + 4 = 364.

In the equation,

AX + B,

-> A is the LCM of all the given values.
-> B is the remainder.
-> The first number of the form: 90A+4 is 364. Hence, the ans.