Lesson 13ª

HOW DO WE CALCULATE THE LOWEST COMMON MULTIPLE?

We will study two ways to calculate it:
1st.       By breaking the number down into its prime factors.
2nd.      By successive divisions.

3.72           Calculate the l.c.m. for (185,75)

Using the method of breaking down the prime factors, we get:

The l.c.m. for (185,25) = 925

To calculate the l.c.m., we simply need to know that:

We take the factors which are different and the ones which are the same with the highest exponent. If they have the same exponent, then we take one of the factors.

In the last exercise, we see that the two numbers have 5 as a factor.

In this case, we take the one with the highest exponent: :

The different factor is 37.

925 is the smallest number we can divide by 185 and 25 and getting an exact quotient. The remainder is zero.

3.73   Calculate the smallest number we can divide by 234 and 184, getting a remainder of zero:

21528 is the smallest number we can divide by both 234 and 184 getting an exact quotient, or, a remainder of zero.

3.74       Calculate the smallest number we can divide by 20631 and 3887, getting a remainder of zero:

Just in case, here is the solution:

There is only one different factor: 3.
From the common factors, 13 and 23, we take the ones with higher exponents.
268203 is the smallest number we can divide by both 20631 and 3887 getting an exact quotient, or, a remainder of zero.

3.75    Calculate the l.c.m. for (375,135)