×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

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

2 Answers

Answer:

Explanation:

Multiples of #8# are #{8,16,24,32,40,48,56,64,72,80,88,96,104,112,color(red)120,....}#

Multiples of #10# are #{10,20,30,40,50,60,70,80,90,100,110,color(red)120,....}#

Multiples of #12# are #{12,24,36,48,60,72,84,96,108,color(red)120,....}#

Hence common multiples are #{120,240,----}#

and Least Common Multiple is #120#

Jan 10, 2018

The general rule is to decompose the numbers into prime factors and then the lcm in the product of all factors raised to the highest power found in those numbers.

#8=2^3#

#10=2xx5#

#12=2^2xx3#

#lcm(8,10,12)= 2^3xx3xx5=120#