Question

Find the greatest 4 digit number
which is exactles divisible by 30,
40,60 and 15
​

Answer 1

$\sf{\underline{We\:know\:that:}}$

The Greatest number of four digits is 9999.

To find the greatest number of 4 digit:
We have to find the L.C.M of 30, 40, 60, 15.

$\sf{\underline{Prime\:factorization:}}$

$\boxed{\sf{30}}$

$\implies$ $\sf{ 2 \times 3 \times 5}$

$\boxed{\sf{40} }$

$\implies$ $\sf{2 \times 2 \times 2 \times 5 = {2}^{3} \times 5}$

$\boxed{\sf{60} }$

$\implies$ $\sf{2 \times 2 \times 3 \times 5 = {2}^{2} \times 3 \times 5}$

$\boxed{\sf{15} }$

$\implies$ $\sf{ 3 \times 5}$

$\sf{\underline{L.C.M\:of:}}$ $\sf{30, 40, 60, 15}$

$\implies$ $\sf{ {2}^{3} \times 3 \times 5}$

$\implies$ $\sf{2 \times 2 \times 2 \times 3 \times 5}$

$\implies$ $\sf{ 8 \times 3 \times 5}$

$\implies$ $\sf{24 \times 5}$

$\implies$ $\boxed{\sf{ 120}}$

$\sf{\underline{Now:}}$

Divide the largest 4 digit number 9999 by 120.

$\sf{\underline{Note:}}$ Check this attachment.

$\sf{\underline{Remainder:}}$ $\boxed{\sf{39}}$

$\sf{\underline{Now:}}$

We have to subtract the remainder from 9999.

$\boxed{\sf{9999 - 39 = 9960}}$

$\sf{\underline{Hence:}}$

9960 is the required greatest 4 digit number, which is exactly divisible by 30, 40, 60 and 15.

Answer 2

Answer:

9960

Step-by-step explanation:

the L.C.M of 30,40,60 and 15 is 120

the greatest four digit number is 9999

dividing 9999 by 120 we get remainder 39

9999 -39

9960