find the greatest number of four digits which is exactly divisible by 15 24 and 36

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Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

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Question

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Medium Open in App

Updated on : 2022-09-05

The greatest four digit number =9999

Solution Verified by Toppr

we can get the required number by following steps:

step 1 : Divide 9999 by LCM of 15,24 and 36

Step 2 : Subtract result of step 1 from 9999.

Prime factorization :

15=3×5 24=2 3 ×3 36=2 2 ×3 2 LCM (15,24,36)= 2 3 ×3 2 ×5=360

Step 1 :  Dividing 9999 by 360, we get 279 as remainder.

Step 2 : subtract 279 from 9999

9999−279=9720

the greatest number of four digit which is exactly divisible by 15,24 and 36 is 9720.

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Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Byju's Answer Standard X Mathematics

Method of Finding LCM

Find the grea... Question

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Open in App Solution Sol:

Prime factorization:

15 = 3 x 5 24 = 2^3 x 3 36 = 2^2 x 3^2

LCM = product of greatest power of each prime factor involved in the numbers = 2^3 x 3^2x 5=360

Now, the greatest four digit number is 9999.

On dividing 9999 by 360 we get 279 as remainder.

Thus, 9999 – 279 = 9720 is exactly divisible by 360.

Hence, the greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.

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Find the greatest of 6 digit exactly divisible by 24 15 and 36

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Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Answer: Using prime factorization: 15 = 3 × 5 24 = 23 × 3 36 = 22 × 32 LCM = 23 × 32× 5 LCM = 360 The greatest four-digit number is 9999. Divide 9999 by 360, 279 – remainder 9999 – 279 = 9720 is exactly divisible by 360. The greatest number of […]

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

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