Question

Which is the LARGEST 3-digitnumber that leaves aremainder 1 when divided by3, 4 and 5? *​

Answer 1

Answer:

981 is the number which satisfies both the criteria.

Answer 2

Answer:

Given,

The largest 3 digit number which when divided by 3, 4 or 5, leaves 1 as a remainder

LCM

Firstly, we will need to find the LCM of 3, 4 and 5

LCM of 3, 4 and 5

= 60

Process

So, any multiple of 60 is divisible by 3, 4 and 5

Now, we need to find the largest 3 digit number divisible by 60 and add 1 to it to obtain our answer

Multiples of 60

60 × 1 = 60

60 × 2 = 120

60 × 3 = 180

60 × 4 = 240

(Continue this till 15)

60 × 15 = 900

60 × 16 = 960

60 × 17 = 1020

We see that 960 is the largest 3 digit multiple of 60

Now, we just need to add 1 to it. So,

960 + 1 = 961

Checking

961 ÷ 3

Quotient = 320

Remainder = 1

961 ÷ 4

Quotient = 240

Remainder = 1

961 ÷ 5

Quotient = 192

Remainder = 1

Conclusion

So, the answer is 961