Hcf and lcm

Question

largest four digit number which divisible by 12or 16 or 18 and leaves remainder 1.but divided by 17 remainder is 0

Comments

7633

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How do you calculate this? @Kushagra Chatterjee

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At first calculate the largest 4 digit number which leaves remainder 1 when divided by 12,16 or 18

Step 1: Calculate LCM (12,14,16) = 144

Step 2: divide 9999 by 144 and calculate the remainder

9999 = 144* q + 63

Hence the largest 4 digit number divisible by 12,16 or 18 = (9999 - 63) = 9936

So, the largest 4 digit number which leaves remainder 1 when divided by 12,16 or 18 is 9937

Now, calculate the largest 4 digit number which is of the form 144 k + 1 and divisible by 17.

Now, since 144 k + 1 is divisible by 17 so we have the number 144k leaves remaider 16 when divided by 17.

Now, since 144 leaves remainder 8 when divided by 17 so we have the number k leaves remainder 2 when divided by 17.

Now, 9936 = 144 * 69

The nearest number which is less than 69 and leaves remainder 2 when divided by 17  is 53.

So, the reqd number is 144 * 53 + 1 = 7633.