Question

What is the least common multiple of 7 and 24?

Answer 1

`168`

Explanation:

By doing the Prime factorization:
`24=2xx2xx2xx3`
`7=7`
And since there's isn't any common factor We need all the prime factors listed
`7xx2xx2xx2xx3=168`

Answer 2

A teacher will expect the prime number method. Just for the hell of it this is a different approach!

168

Explanation:

We have two numbers ; 24 and 7

I am going to count the 24's. However lets look at this value.

24 can be 'split' into a sum of 7's with a remainder. So each 24 consists of:

`24=(7+7+7+3)`

If we sum columns of these we will get the 3 summing to a value into which 7 will divide exactly. When this happens we have found our least common multiple.

REMEMBER WE ARE COUNTING THE 24's

`" count "color(white)("dd") "The 24's"`
`color(white)("ddd") 1color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 2color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 3color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 4color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 5color(white)("ddd")(color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 6color(white)("ddd")( color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)`
`color(white)("ddd") 7color(white)("ddd")ul( (color(white)(.)7+color(white)(.)7+color(white)(.)7+color(white)(.)3)larr" Add"`
`color(white)("ddddddd.")49+49+49+ubrace(21)`
`color(white)("dddddddddddddddddddd")darr`
`color(white)("dddddddddddddd")" exactly divisible by 7"`

We have a count of 7 so the value is `7xx24 = 168`