# What is the least common multiple of 8, 10, 12?

What is the least common multiple of 8, 10, 12?
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Sydnee Villegas
Step 1
Multiples of 8 are $\left\{8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,....\right\}$
Multiples of 10 are $\left\{10,20,30,40,50,60,70,80,90,100,110,120,....\right\}$
Multiples of 12 are $\left\{12,24,36,48,60,72,84,96,108,120,....\right\}$
Step 2
Hence common multiples are $\left\{120,240,----\right\}$
and Least Common Multiple is 120
###### Did you like this example?
Ezekiel Yoder
Step 1
The general rule is to decompose the numbers into ' factors and then the lcm in the product of all factors raised to the highest power found in those numbers.
$8={2}^{3}$
$10=2×5$
Step 2
$12={2}^{2}×3$
$\mathrm{lcm}\left(8,10,12\right)={2}^{3}×3×5=120$