Question

20. Determine the greatest 3 digit number exactly divisible by 10, 15 and 20.
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Answer 1

Answer:

Answer:

Given

Three numbers 8,10 and 12

Find out

We need to find out the largest 3-digit number which is exactly divisible by 8, 10 and 12

Solution

To find out the largest 3-digit number which is exactly divisible by 8, 10 and 12

first let us calculate the L.C.M 8, 10 and 12

L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5

Hence, LCM of 8, 10, 12 = 120

We have to find the greatest 3 digit multiple of 120

Therefore,  the number is

120 x 8 = 960

120 x 10 = 1200

120 x 12 = 1440

The 1200 and 1440 are not 3-digit numbers.

Hence, the greatest 3- digit number exactly divisible by 8, 10 & 12 is 960.

Verification

Now, let us check whether 960 is divisible by 8, 10 and 12.

960 ÷ 8 = 120

960 ÷ 10 = 96

960 ÷  12 = 80

So the greatest 3-digit number is 960.

Step-by-step explanation:

Answer 2

Answer:

LCM of (10, 15, 20)

⇒ 5 × 2 × 3   = 30

⇒ Largest 3-digit number = 999

divide 999 by LCM of given number

⇒ We get remainder = 33 ( approx )

⇒ So, to divide completely subtract it from (999 - 33 = 966)

∴ 966 is the largest three digit number which is completely divided by the given numbers.