Question

Determine the largest 3 digit number exactly divisible by ? 6,10 and 12

Answer 1

Answer:

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.

Step-by-step explanation:

Answer 2

Given

• Numbers = 6, 10 and 12

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To find

• The largest 3 digit number exactly divisible by 6, 10 and 12.

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Solution

• Let us find the LCM of 6, 10 and 12.

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$\Large{ \begin{array}{c|c} \tt 2 & \sf{ 6 , 10 , 12} \\ \cline{1-2} \tt 2 & \sf { 3 , 5 , 3} \\ \cline{1-2} \tt 3 & \sf{ 1 , 5 , 1} \\ \cline{1-2} \tt 5 & \sf{ 1 , 1 , 1} \end{array}}$

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$\tt\longmapsto{LCM = 2 \times 2 \times 3 \times 5}$

$\tt\longmapsto{LCM = 60}$

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★ Now, we have to find the greatest 3 digit multiple of 60.

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★ Therefore,

• The number is 60 × 16 = 960

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Hence, the greatest 3- digit number exactly divisible by 6, 10 & 12 is 960.

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Verification

★ Now, let us check whether 960 is divisible by 6, 10 and 12.

$\tt:\implies{960 ÷ 6 = 160}$

$\tt:\implies{960 ÷ 10 = 96}$

$\tt:\implies{960 ÷ 12 = 80}$

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$\underline{\underline{\mathcal{\orange{Verified}}}}$

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• So the greatest 3-digit number is 960.

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