How do you find the LCM of any number without guess and check?

1 Answer
Oct 8, 2017

Follow the following procedure.

Explanation:

Let the two numbers be say 8 and 36.

Write out the prime factors of each number.

8=color(red)(2xx2)xx2

36=color(red)(2xx2)xx3xx3

Observe that color(red)(2xx2) are common to both. Observe this is HCF of two numbers.

What are others? color(purple)2 is remaining in first and color(green)(3xx3) remain in second.

Multiply all to get LCM i.e. LCM is

color(red)(2xx2)xxcolor(purple)2xxcolor(green)(3xx3)=72

Simiilarly, let the three numbers be 8, 12 and 20 and then

8=color(red)(2xx2)xx2

12=color(red)(2xx2)xx3

20=color(red)(2xx2)xx5

Observe that color(red)(2xx2) are common to the three. Observe this is HCF of three numbers.

What are others? color(purple)2 is remaining in first, color(green)3 remains in second and color(blue)5 remains in the third number.

LCM is color(red)(2xx2)xxcolor(purple)2xxcolor(green)3xxcolor(blue)5=120