Find the greatest 4 digit number which when divided by 20, 24 ,45 leaves a remainder 18 in each case
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Answer:
Step-by-step explanation:
Given numbers,
20 , 24 and 45
Prime factorization of
20=2²×5
24=2³×3
45=3²×5
LCM=product of each prime factor of highest power
LCM=2³×3²×5=360
Greatest four digit number=9999
greatest four digit number divisible by all given numbers=9999-remainder when 9999 is divided by LCM of given numbers
greatest four digit number divisible by given numbers=9999-279=9720
Given that,
required number when divided by 20 , 24, 45 leaves remainder 18.
Therefore,required number=9720+18=9738
Hence greatest four digit number when divided by 20,24 and 45 is 9738.
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