The least number which when decreased by 7 is exactly divisible by 12,16,18,21 and 28 is ____.

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Solution

Let us assume the number is xSo x-7 is divisible by 12,16,18,21 and 28(x-7) is the LCM of the following numbers: i.e. 1008x-7=1008x=1015

|2 12, 16, 18, 21, 28
|7 6, 8, 9, 21, 14
|3 6, 8, 9, 3, 2
|2 2, 8, 3, 1, 2
| 1, 4, 3, 1, 1
LCM=273243=1008LCM=273243=1008
Required number =1008+7=1015=1008+7=1015.

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Let us assume the number is xSo x-7 is divisible by 12,16,18,21 and 28(x-7) is the LCM of the following numbers: i.e. 1008x-7=1008x=1015
\|2 12, 16, 18, 21, 28 \|7 6, 8, 9, 21, 14 \|3 6, 8, 9, 3, 2 \|2 2, 8, 3, 1, 2 \| 1, 4, 3, 1, 1 LCM=273243=1008LCM=273243=1008 Required number =1008+7=1015=1008+7=1015.