Factors and Multiples

LCM by Listing

Find the least common multiple of 4 and 6 by listing multiples of each number until a shared value appears. LCM(4, 6) = 12.

Example

Find the least common multiple of 4 and 6 by listing multiples.

highlighted = computed this step

Step 1 — Set up

Set up the numbers to test.

LCM(4,6)\mathrm{LCM}( 4 , 6 )
List multiples of 4 and 6; look for the first match.multiples of 4not listed yetmultiples of 6not listed yetfirst matchwait for both listsLCM = --

Step 2 — List first multiples

List multiples of 4 up to the first match.

multiples of 4:4,8,12\mathrm{multiples\ of}\ 4 : \hl{4}, \hl{8}, \hl{12}
List multiples of 4 up to the first match.multiples of 44812multiples of 6not listed yetfirst matchwait for both listsLCM = --

Step 3 — List second multiples

List multiples of 6 up to the first match.

multiples of 6:6,12\mathrm{multiples\ of}\ 6 : \hl{6}, \hl{12}
List multiples of 6 up to the first match.multiples of 44812multiples of 6612first matchwait for both listsLCM = --

Step 4 — Result

The least common multiple is 12.

LCM(4,6)=12\mathrm{LCM}( 4 , 6 )= \hl{12}
The first shared multiple is 12.multiples of 44812multiples of 6612first match12LCM = 12
least-common-multiple The LCM of two numbers is the smallest number both divide into evenly. List multiples of each (4, 8, 12, … and 6, 12, …) and find the first match. You use the LCM when adding fractions with different denominators.