Question

Determine two numbers nearest to 3000 exactly divisible by 5 7 14 15​

Answer 1

2940 and 3150

Explanation:

Numbers are 5, 7, 14, 15

LCM of 5, 7, 14, 15 is 14*15 = 210 since 14 = LCM of 7 and 14 and 15 = LCM of 5 and 15

Dividing 3000 by LCM of given numbers:

• 3000/210 ≈ 14.28

Nearest multiples of 210 are 14 and 15

Therefore the nearest numbers are:

• 14*210 = 2940

and

• 15*210 = 3150

Answer 2

The numbers are

2730 and 2940

Explanation:

From the question we are finding any two given numbers that's closest to 3000 exactly divisible by 5 , 7 , 14 and 15

Which means that the numbers above can exactly divide those two numbers without a remainder.

The numbers closest to 3000 which have this property are

2730 and 2940

Proof

For 2730

2730 ÷ 5 = 546 no remainder

2730 ÷ 7 = 390 no remainder

2730 ÷ 14 = 195 no remainder

2730 ÷ 15 = 182 no remainder

For 2940

2940 ÷ 5 = 588 no remainder

2940 ÷ 7 = 420 no remainder

2940 ÷ 14 = 210 no remainder

2940 ÷ 15 = 196 no remainder

The above proof shows that the answers are true

Hope this helps you