Question

The greatest number less than 10,000 which is exactly Divisible by 48, 60, 64 is

Answer 1

Answer:

9600

Step-by-step explanation:

L.C.M of 48,60,64 is

2 × 2 × 2 × 2 × 3 × 5 × 4 = 960

∴The greatest number less than 10,000 which is exactly Divisible by 48, 60, 64 is 9600.

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Answer 2

9600 is the greatest number less than 10,000 which is exactly Divisible by 48, 60, 64

Solution:

Given that,

We have to find the greatest number less than 10,000 which is exactly Divisible by 48, 60, 64

Step 1:

FIND THE LCM OF 48 , 60 , 64

List all prime factors for each number.

Prime Factorization of 48 is:    2 x 2 x 2 x 2 x 3  

Prime Factorization of 60 is:   2 x 2 x 3 x 5  

Prime Factorization of 64 is:    2 x 2 x 2 x 2 x 2 x 2

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 2, 2, 2, 3, 5

Multiply these factors together to find the LCM

LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 = 960

LCM = 960

STEP 2:

We know that,

Largest 4 digit number = 9999

When we divide 9999 by 960,

Remainder = 399

Thus, the required number = 9999 - 399 = 9600

Thus 9600 is the greatest number less than 10,000 which is exactly Divisible by 48, 60, 64

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