what's the least common multiple of 8, 10, and 7?

Answer 1

****left hand column in box are the prime numbers that go into 8 and the right hand column are the amount of times that the number goes into the prime number

Basically you have to take the number or numbers in which you are looking for their LCM and work through prime numbers and see which prime number goes into it and then how many times it goes into it as well…. So with 8 … the first prime number that we know of is 2… and 2 goes into 8, and it goes into 8 4 times… so to help… you can make a box.. when you are done writing down the prime number, and the amount of times it goes into the number ( in our case it is 8)… you then look at the number of times it went into ( and in our case that number is 4)… so now we look for the prime numbers in 4 . the first one is 2… and it goes into 2 times. Then once again, just as we did with 4, we do with two again, and 2 is the frst prime number, but 2 is a prime number, and as you can see 2 goes into itself once. Once you are unable to find any more prime numbers, then you are finshed with that number. so now lets go to 10.

8
2 4
2 2
2 1

Now let’s find 10
We need to find the first prime number that goes into 10, and that is 2. so we put two in the box.. Now how many times does 10 go into 2?. 5 times. Now we have to find the first prime number that goes into 5. 5 is a prime number so the first prime number that goes into it is 5… and 5 goes into 5 .. one time.

10

2 5
5 1

Now lets try 7

7

7 1

The only prime number that goes into 7 is seven.

**** Look in the left hand colomns and write down what numbers are there ( if a number is written more than once than write it as only appearing once) … so you can see that the numbers that appear are 2 5 and 7. so now make another box and write 2 5 and 7 on the top. Then on the left colomun down below write the numbers that you were solving. Now… go back to each box and take all the numbers from the left hand colomn and literally place them in the number coluimns that it belongs ( now you literally take each number… if there is a multiple of a number, you use it). so with the number 8 – it has 3 2’s… sooo you write - read going across.
THEN…. Do the same thing for the rest of the numbers

2 - 8 has 3 2's... so its 2*2*2. 10 has one two so 2 and 7 has none

5 - 8 has none. 5 has one so 5. and 7 has none

7 - 8 has none 5 has none and 7 has one so 7. now you take the biggest number with each factor, so the biggest in 2 is 2*2*2.... and 5 and 7 onyl have one so just take those numbers.

Now what you do is take the largest number in the clomumns reading down… so colomun with 2, the biggest one is 2*2*2. the other numbers only have one number in it so just take them. so our result is

2*2*2*5*7 when you multiply them all together you get 280

I know this may look confusing and sound confusing but if you read it slowly, and work at it it really helps and comes in handy!. Good luck

Answer 2

7, 8 and 10
7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
10, 20, 30, 40, 50, 60, 70, 80, 90, 100
apparently, there are none up to 100
so lets try another way.

7 * 8 * 10 = 560. This is A multiple, but it isnt the least common.

Lets try diving it by 2 to see if it still follows the constraints.
560/2=280
280/7 = 40
280/8 =35
280/10 = 28
it works, lets try going even further, 1/4th of 560.
140
140/7 = 20
140/8 = 17.5
140/10 = 14

17.5 is not a whole number, thus no worky. So 280 was the highest solution.

280

Answer 3

The multiples of the biggest number, 10, are 1, 2, 5, and 10. The only one of these that's common to both 8 and 7 is 1.

Answer 4

8*5*7 (the factor of 2 you need to divide by 10 is "in" the 8) = 280

280/10=28
280/7=40
280/8=35

Answer 5

ok, since one of the numbers is ten it MUST end with a zero.then you think of the leaset common multiple of 7 and 8., which i think is 56. But you have to add a zero for 10 and you get 560.

Now, this could be the answer.....but if you divide it in half you get 280, which works too.

Your answer is......280!

Answer 6

I think the least common denominator is 560 because 7,8, and 10 each divide into that number equally

Answer 7

280

Answer 8

8 ... 1,2,4,8
10.. 1,2,5,10
7.....1,7

lcm=1