Math, asked by 333brainly, 11 months ago

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

Answers

Answered by Anonymous
11
\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.
Attachments:

Swarnimkumar22: well Explained
Anonymous: Thank you!
Answered by shanthini5343
1

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

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