Question

Find the least number of five digits which is exactly divisible by 32, 36, and 45

Answer 1

Answer:

Answer is 10080

Step-by-step explanation:

Given : The least number of five digits which is exactly divisible by 32,36 and 45.

To find : The least number ?

Solution :

The least 5-digit number is 10000.

Now, we find the LCM of 32,36 and 45.

2 | 32 36 45

2 | 16 18 45

2 | 8 9 45

2 | 4 9 45

2 | 2 9 45

3 | 1 9 45

3 | 1 3 15

5 | 1 1 5

| 1 1 1

LCM(32,36,45)=2\times 2\times 2\times 2\times 2\times 3\times 3\times 5LCM(32,36,45)=2×2×2×2×2×3×3×5

LCM(32,36,45)=1440LCM(32,36,45)=1440

Divide 10000 by 1440 so that we get the remainder,

10000 = 6\times 1440 + 136010000=6×1440+1360

Remainder is 1360.

The required number is

=10000+(1440-1360)=10000+(1440−1360)

=10000+80=10000+80

=10080=10080