Question

find the greatest number of 6 digit which on division by 42 45 48 56 and 60 leaves 12 as remainder in each case​

Answer 1

Answer:

Let us write the prime factorisation of the given numbers

42 = 2×3×7

45 =×5

48 =×3

56 =×7

60 =×3×5

LCM of these numbers = product of the highest power of each prime factor

=××5×7

=5040

Logically,any number which is divisible by all 5 above mentioned numbers must be a multiple of their LCM which is 5040

We want the largest 6 digit number of that sort

the largest 6 digit number would be 999999 which when divided by 5040 gives

999999/5040=198.4125

So the largest six digit number divisible by 5040 without remainder is 5040×198 = 997920

when we add remainder 12 to this we get 997932

Hence 997932 is the largest six digit number which when divided by 42,45,48,56,60 gives remainder 12.

Answer 2

Answer:

Step-by-step explanation: