Question

Find the greatest 3-digit number which when divided by 75, 45 and 60 leaves
(i) The remainder 4 in each case.
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Answer 1

Step-by-step explanation:

Given:-

Numbers are 75, 45 and 60.

To find:-

Find the greatest 3-digit number which when divided by 75, 45 and 60 leaves

Find the greatest 3-digit number which when divided by 75, 45 and 60 leaves(i) The remainder 4 in each case.

Solution:-

Given numbers are 75,45 and 60

The greatest number which divided by 75,45,60 =The LCM of 75,45,60

75=3×5×5

45=3×3×5

60=2×2×3×5

LCM (75,45,60)=2×2×3×3×5×5=900

LCM of 75,45 and 60 =900

900 is the greatest three digit number which divided by 75,45,60 exactly.

Now given that it leaves the remainder

=>900+4

=>904

Answer:-

The required number=904