what is the lcm(lowest common multiple) of 240 and 9?

Question

i cant figure this problem out HELP

Answer 1

If you know how to find GCD (greatest common divisor) you can use the following trick:

LCM = 240 * 9 / GCD

In this case, the GCD is 3, so LCM = 240 * 9 / 3 = 720.




You can find the GCD as follows.
Divide the largest number by the smallest, and write down the remainder.

Replace the largest number by the smallest, and the smallest number by the remainder. Repeat this until the remainder is zero.

[ > 240 / 9 = 26, remainder 6 ]
[ > 9 / 6 = 1, remainder 3 ]
[ > 9 / 3 = 3, remainder 0 ]

The last number you used for dividing is the GCD! This marvelous trick was invented by the Greek scientist Archimedes.



One other example: what is the LCM of 672 and 210?

First we find the GCD:
[ > 672 / 210 = 3 R. 42 ]
[ > 210 / 42 = 5 R. 0 ]
So the GCD is 42.
[ > Check: 672 / 42 = 16; 210 / 42 = 5 ]
Now we find the LCM.
[ > LCM = 672 * 210 / 42 = 672 * 5 = 3360 ]
So the LCM is 336.
[ > Check: 3360 / 672 = 5; 3360 / 210 = 16 ]

Answer 2

The first answer someone gave you was the greatest common divisor, not the least common multiple. Here is a method to find the LCM.

Prime factor 240 = 2x2x2x2x3x5 and
9 = 3x3
Now the LCM must have the factors of 240 and the factors of 9, but don't repeat any common factors. So, the LCM = 2x2x2x2x3x5x3. You don't need 3 factors of 3 since the most factors of 3 that are needed is 2 (for the 9)

Now, multiply 2x2x2x2x3x3x5 = 720 = LCM.

You will notice that a 3 is the only common factor. Therefore, 3 is the GCF (greatest common factor of 240 and 9) Prime factoring can be used to find both the LCM and the GCF.

Answer 3

720 is the least common multiple

just keep checking multiples of 240 until you get one divisible by 9

240 ... no, 480 ... no , 720 ... yes!

In response to the other answer,
3 is the greatest common divisor, not the least common multiple

Answer 4

3 if you don't count 1

240/3=80
9/3=3

Answer 5

it's 720, Trust me on this.