What is the smallest number which when divide by 7,8 and 9 leave a remainder of 5,4 and 2 resp.Please explain the approach.TIA?

we need a number that is 7n+5, 8n+4 and 9n+2. We combine them 2 at a time.

7n+5=8n+4

The smallest such number where these two notations would overlap is 12

Therefore the combined number we are seeking is 56n+12

we combine 9n+2 to it now

56n+12=9n+2

these notations would coincide at 236

Therefore the smallest number which fulfills all above criteria is 236

@shankar bhayankar ... How can we say that the number will be of same multiple 'n' for all the three divisors?

i.e., how could we assume the number as multiple of 'n' with 7,8,and 9? It can be different quotients as well right, when divided by these divisors.

Please correct me if I am wrong