Question

Q 12 Find the least number which on decreasing by 20 is exactly divisible by 18, 21, 28 and
30​

Answer 1

Answer:

To find the least number which on decreasing by 20 is exactly divisible by 18,

21, 28, 35, first we have to take the L.C.M. of 18, 21, 28, 35

L.C.M. of 18, 21, 28, 35

        _______________

    2 | 18, 21, 28, 35

       |_______________

    2 |   9, 21, 14, 35

       |_______________

    3 |   9, 21,  7,  35

       |_______________

    3 |   3,  7,   7,  35

       |_______________

    5 |   1,  7,   7,  35 

       |_______________

    7 |   1,  7,   7,   7

       |_______________

       |   1,  1,   1,   1

       |

L.C.M. of 18, 21, 28, 35 = 2*2*3*3*5*7

= 1260

Now, the required number is 1260 + 20 

= 1280

Therefore, 1280 is the least number which on decreasing by 20 is exactly divisible by 18, 21, 28, 35

Let us check it.

1280 - 20 = 1260

1) 1260 ÷ 18 = 70

2) 1260 ÷ 21 = 60

3) 1260 ÷ 28 = 45

4) 1260 ÷ 35 = 36

The answer is correct.

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