Question

find the smallest number which when divided by 33 and 153 leaves a remainder of 3 in each case​

Answer 1

To Find :-

The smallest number on divided by 33 and 153 leaves 3 as a remainder .

Solution :-

We have to find the smallest number [LCM ]

Firstly let's find out the factor of 33 and 153 :-

$\sf{\implies 33 = 3 \times 11 }$

$\sf{\implies 153 = 3 \times 3 \times 17 }$

Now LCM of these two numbers is :-

$\sf{\implies LCM \; = 3 \times 3 \times 11 \times 17 }$

$\sf{\implies LCM \;= 1683 }$

Now we know that the number leaves remainder of 3 also , so

$\sf{\implies \; Number = 1683 + 3 \rightarrow 1686 }$

$\boxed{\sf{\red{Number\:is\: 1686}}}$

Verification :-

→ 1686 = 153 × 11 + 3

→ 1686 = 33 × 51 + 3 .