How to find the least common multiple in a number

Well, there are a few ways.

The easiest would be to factor the two(or more) numbers you want to find the LCM of and only consier the prime factor with the highest degree. An example of this is if you wanted to find the least common multiple of 30 and 28, you first factor them:

So then you only consider the highest factors between them:

Another way of doing it is:

This is essentially the same as the step above, but it requires (I feel) more steps and thinking. It works because when you multiply 30 and 28, you actually "overcount" their factors in a sense. That's because you multiply the numbers they share, like 4 and 2, instead of just considering the 4. When you divide by the greatest common divisor between the two, you account for this by removing any factor they share. So now you only consider the highest between the two, which is what we want. The second method works for numbers that are too big to reasonably factor. You can use the Euclidean algorithm to make finding the GCD much easier than it would be to find the factors. Either way works though.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: