Question

Telegraph poles occur at equal distances of $220m$ along a road and heaps of stones are put at equal distances of $300m$ along the same road. The first heap is at the foot of the first pole. How far from it along the road is the next heap which lies at the foot of a pole?

Answer 1

Hint: First, we have to define the two distance values from the telegraph which are $220m$and $300m$
But the first telegraph poles occur at a distance of two twenty meters along that road where the second one occurs three hundred meters at the same road.
We have to find how long the next heap is, thus we are going to use the method of LCM to find the required answer.

Complete step-by-step solution:
Since the first heap is the foot of the first pole is given in the question.
Now make use of the least common multiple methods, which is finding the common multiple terms with the given two or more than two numbers, and then we will find which of the common terms are least.
Thus, first making the numbers given into the prime factors,$200$ can be written in the form of a prime factor as $200 = 11 \times 20$here as we see the eleven is the prime but not twenty.
Thus convert the twenty into the prime factors we get $20 = 4 \times 5$(four is not the prime but five is prime)
Again, convert the four into the prime we get$4 = {2^2}$.
Hence, we get the prime factor of the number$200 = 11 \times 5 \times {2^2}$.
Similarly, for the number three hundred, we have the prime factor as$300 = 3 \times {5^2} \times {2^5}$.
Therefore, we have total terms as $11 \times 5 \times {2^2},3 \times {5^2} \times {2^5}$ . Now we will see which of the terms are common and also the least.
Thus, we get two, three, five, and eleven. Where the highest factor of three and five are two times.
Hence the LCM of the two numbers $220m$and $300m$is${2^2} \times 3 \times {5^2} \times 11 = 3300$.
Therefore at $3300m$ next heap of the stones will lie at the foot of the pole.

Note: Since in the given question, we need a method called LCM used, but there are also two methods similar to this which are GCD the greatest common divisor, and HCF the highest common factor.
There is also a common formula for GCD and LCM is $\gcd (a,b) \times lcm(a,b) = a \times b$