find the smallest number which when increased by 3 is divisible by 21 28 36 and 45
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Consider the number : X
→ ( X + 3 ) is divisible by : 21 , 28 , 36 , 45
=> ( X + 3 ) has all factors of : 21 , 28 , 36 , 45
=> ( X + 3 ) is divisible by : LCM( 21 , 28 , 36 , 45 )
=> ( X + 3 ) is divisible by : 36 x 7 x 5 = 36 x 35 = 1260
=> X = ( 1260k - 3 )
=>Smallest such number = - infinity
However, smallest such number in the NATURAL NUMBER set is
= ( 1260 x 1 - 3 ) = 1257 [ the desired number ]
→ ( X + 3 ) is divisible by : 21 , 28 , 36 , 45
=> ( X + 3 ) has all factors of : 21 , 28 , 36 , 45
=> ( X + 3 ) is divisible by : LCM( 21 , 28 , 36 , 45 )
=> ( X + 3 ) is divisible by : 36 x 7 x 5 = 36 x 35 = 1260
=> X = ( 1260k - 3 )
=>Smallest such number = - infinity
However, smallest such number in the NATURAL NUMBER set is
= ( 1260 x 1 - 3 ) = 1257 [ the desired number ]
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