Question 62

Find the smallest number such that when it is divided by 5, 6 and 8 it leaves a remainder 3 in each case.

Solution

Note : The smallest number which when divided by 5,6 and 8 leaves no remainder will be the LCM of 5,6 and 8.

LCM = $$2\times\ 2\times\ 2\times\ 3\times\ 5$$

$$\longrightarrow\ 120$$

Required number = 120 + 3

$$\longrightarrow\ 123$$

$$\therefore\ $$ 123 is the least number which when divided by 5, 6 and 8 gives remainder 3.

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