Question

Find the smallest number when divided by 35, 42 and 70 leaves the remainder 9 in each case.

Answer 1

Answer:

3640 + 7 = 3647.

Step-by-step explanation:

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Answer 2

The smallest number which when divided by 35, 42, and 70 leaves a remainder of 9 in each case is 219.

Given: The numbers 35, 42, and 70.

To Find: The smallest number when divided by 35, 42, and 70 leaves a remainder of 9 in each case.

Solution:

• We are required to find the smallest number, so we shall find the LCM of the given numbers.

• The LCM after being increased by a particular number gives us the lowest number which divides a set of numbers leaving a certain fixed remainder in each case.

Coming to the numerical, we have,

The numbers 35, 42, and 70.

We need to find the smallest number so we shall find the LCM first using the prime factorization method.

Writing the prime factors of the numbers, we get;

35 = 5 × 7

42 = 2 × 3 × 7

70 = 2 × 5 × 7

∴ LCM ( 25, 40, 60 ) = 2 × 3 × 5 × 7

                                    = 210

Now, it is said that the LCM must leave a remainder of 9 always when it is divided by the given numbers, so we shall increase the LCM by 9  so that a remainder of 9 always comes.

So, the increased number is = 210 + 9

                                               = 219

Hence, the smallest number when divided by 35, 42, and 70 leaves a remainder of 9 in each case is 219.

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