document.write( "Question 1090941: Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of 20,25 and 35 respectively? \n" ); document.write( "

Algebra.Com's Answer #705384 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of 20,25 and 35 respectively?
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document.write( "Let N be the number under the question.\r\n" );
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document.write( "Let us consider the number N+5.\r\n" );
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document.write( "Then, according to the condition, the number N+5 leaves the remainders 25, 30 and 40 when divided by 25, 30 and 40, respectively.\r\n" );
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document.write( "It is the same as to say that the number N+5 leaves the remainder 0 when divided by 25, 30 and 40.\r\n" );
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document.write( "The least common multiple (LCM) of the numbers 25, 30 and 40 is 600.\r\n" );
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document.write( " = 1666.67,\r\n" );
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document.write( "therefore, the number N+5 is equal to 1666*600 = 999600.\r\n" );
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document.write( "Then the number N under the question is 999600-5 = 999595.\r\n" );
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