find the greatest number of six digits which on division by 42,45,48,56 and 60 leaves 12 as remainder in each case.
Answers
LCM of 42, 45, 48, 56 and 60 = 5040.
Find the largest 6 digit multiple of 5040.
The largest 6 digit number is 999999.
999999 divided by 5040 gives quotient 198 and remainder 2079.
So 5040 x 198 = 999999 - 2079 = 997920 is the largest 6 digit multiple of 5040.
Add the remainder 12 which is required in the question.
997920 + 12 = 997932.
∴ 997932 is the answer.
If any doubt, divide 997932 by the divisors required. If the same remainder 12 is gotten, it's the right answer. If not, I failed!
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The greatest number of six digits which on division by 42,45,48,56 and 60 leaves 12 as the remainder in each case is 997932.
Given,
Six numbers: 42,45,48,56 and 60.
To Find,
The greatest number of six digits which on division by 42,45,48,56 and 60 leaves 12 as the remainder in each case.
Solution,
The method of finding the greatest number of six digits which on division by 42,45,48,56 and 60 leaves 12 as the remainder in each case is as follows -
Let us calculate the LCM of the given six numbers 42,45,48,56 and 60.
42 = 2 x 3 x 7, 45 = 3 x 3 x 5, 48 = 2 x 2 x 2 x 2 x 3, 56 = 2 x 2 x 2 x 7, and 60 = 2 x 2 x 3 x 5.
So the LCM of 42,45,48,56 and 60 is .
But 5040 is a four-digit number.
Now we know that 999999 is the largest six digits number.
Now we will divide 999999 by 5040.
After dividing 999999 by 5040, the quotient is 198 and the remainder is 2079.
So, is the greatest multiple of
So, 997920 is also the greatest common multiple of 42,45,48,56 and 60 among six-digit numbers.
Now we will add 12 to 997920.
So, we can conclude if 997932 is divided by 42,45,48,56 and 60, the remainder is 12 in each case.
Hence, 997932 is the greatest possible six-digit number which on division by 42,45,48,56 and 60 leaves 12 as the remainder in each case.
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