13) Which is the greatest five digit number when divided by 28 ,35 or 45 leaves remainder 4 in each case ?
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13) Which is the greatest five digit number when divided by 28 ,35 or 45 leaves remainder 4 in each case ?
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The difference between the divisor and the remainder is same in all the cases which is 6
STEP 1:
LCM OF DIVISORS
LCM OF( 9,12,24,45) IS 360
STEP 2:
We know the largest five digit number is 99999
Now to find the largest five digit number which satisfy the given conditons then do the following
A) 360*N-6
N, is the quotient of 99999/360
U will get the answer as 360*277–6= 97214
B) Divide 99999/360
U will get remainder as 279
SUBTRACT 279 FROM 99999 WHICH IS 99720
Now 99720–6= 97214 which will be ur answer
OR
3=x mod 9
6=x mod 12
18=x mod 24
39=x mod 45
Modulo values in each case is number-6.
Number is LCM-6
=9*4*2*5–6
=360–6
=354
To find largest five digit number, 360x-6 where x is integer.
100000/360= 10000/36=277
Largets 5 digit number =360*277–6
=99720–6
=99714
This one was a bit tricky though.
Hope it was simple illustration.
Good luck and don't forget to upvote if you liked how it was solved.
Answer:
Step-by-step explanation:
8=2314=2×718=2×3224=23×3
48=24×3
L.C.M. (8, 14, 18, 24, 48)=24×32×7=1008
1008+6=1014
∴1014 is the smallest 4 digit number which leaves a remainder of 6
When divided by 8, 14, 18, 24 and 48
The largest 5 digit number is 99999.
99999÷1014≈98.61
1014+1008×98=99798is the largest integer which leaves a remainder
of 6 when divided by 8, 14, 18, 24 and 48
99798=12474×8+6
99798=7128×14+6
99798=5544×18+6
99798=4158×24+6
99798=2079×48+6
Hope it helps u!...