Lowest Common Multiples

In a world where nature's symphony turns sinister, they thought they knew the rhythm of the cicadas. But when two ancient broods converge, they'll face a swarm like never before! By learning about lowest common multiples, we can determine when they will next strike together! There are times you will need to apply more than one multiple to a situation or problem, like determining when two different broods of periodical cicadas will emerge at the same time. To do this, you would need to find their lowest common multiple. This is the smallest number that can be divided by both numbers without a remainder. There are two methods for finding the ; list of multiples, which is useful for smaller numbers, and prime factorisation, which is useful for larger numbers. Let's see how the list of multiples strategy works with the numbers four and ten. We list the multiples of each, (...) then find the lowest values in common and circle them. Looking at the multiples of four and ten, twenty is the lowest common multiple. Now let's look at prime factorisation, which helps with larger numbers. Let's find the of twelve and eighteen. Twelve is the product of two and six. Six is further broken down to two times three. Eighteen can be broken down into two and nine and nine has the prime factors three and three. For the next step, create a simple table, and match the like factors, and leave a space where there are no like factors. Then we use only one value from each column, so here it would be two, two, three and three. Find the by multiplying two times two, times three, times three, which is thirty-six. Back to our original problem; periodical cicadas emerge either every thirteen or seventeen years. You may notice that both thirteen and seventeen are already prime numbers since their factor pairs are one and itself! When this happens, we can find the lowest common multiple of prime numbers by multiplying them together. Thirteen multiplied by seventeen is two hundred and twenty-one. The two broods of cicadas will swarm at the same time every two hundred and twenty-one years! To summarise, we can find the lowest common multiple of smaller numbers by listing multiples until we find the first number they have in common. We can use prime factorisation to break down larger numbers to their prime factors, by listing the prime factors in a table and aligning like values and leaving gaps if there are no like values, and multiplying one value from each column to find the . In special cases, you may find that both values are already prime numbers; in this situation, you can just multiply them together to find the ! Brace yourselves for a swarm like never before...in two-hundred and twenty-one years!