Question

Вдоль аллеи через каждые 15 метров посадили кусты шиповника,а через 18 метров-берёзы.Через сколько метров от начала аллеи куст шиповника окажется рядом с берёзой решение

Answer 1

15 = 3*5, 18 = 3*6
НОК(15, 18) = 3*5*6 = 15*6 = 90
Ответ: через 90 м. Шиповник будет 90/18 = 5-ый куст, а береза 90/15 = 6-ая.

Answer 2

НОК (15;18)=90
Ответ: через 90 метров.

Answer 3

Problem Analysis

We are given that along an alley, shrubs of rosehip are planted every 15 meters, and birch trees are planted every 18 meters. We need to determine at what distance from the beginning of the alley the shrub of rosehip will be next to a birch tree.

Solution

To solve this problem, we need to find the least common multiple (LCM) of 15 and 18. The LCM will give us the distance at which the shrub of rosehip will be next to a birch tree.

The LCM of two numbers can be found by multiplying the numbers together and then dividing by their greatest common divisor (GCD).

Let's calculate the LCM of 15 and 18:

Step 1: Find the GCD of 15 and 18.

The prime factorization of 15 is 3 * 5. The prime factorization of 18 is 2 * 3 * 3.

The common prime factors are 3 * 3, which gives us a GCD of 9.

Step 2: Calculate the LCM using the formula: LCM = (15 * 18) / GCD.

LCM = (15 * 18) / 9 = 30.

Therefore, the shrub of rosehip will be next to a birch tree at a distance of 30 meters from the beginning of the alley.

Answer

The shrub of rosehip will be next to a birch tree at a distance of 30 meters from the beginning of the alley.

Explanation

The LCM of 15 and 18 is 30. This means that after every 30 meters along the alley, a shrub of rosehip will be next to a birch tree.