# Find the l.c.m. of 15 and 18

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first we need to factor 15 and 18:

We know tha:

15 = 3*5

18 = 2*3*3

To calculate the L.C.M, we will multiply all uncommon elements and the heighest power of the common element.

Then the L.C.M = (3*3) *2 *5 = 90

==> L.C.M (15, 18) = 90

To check:

90 = **15** * 6

90 = **18** * 5

The LCM of 15 and 18:

We know that LCM(15,18) = (15/HCF)18

We find the HCF:

15 = 3*5

18 = 2*3*3.

The common factors in (3*5) and (2*3*3) is 3, and it is the highest common factor also, as no other factor higher than 3 divide both 15 and 18 together.

Therefore LCM (15,18) = (15/3)18 = 90.

To calculate the least common multiple of 15 and 18, we'll factor 15 and 18 into their prime factors.

15 = 3*5

18 = 2*3*3

Now, we'll consider the different factors from both numbers and we'll multiply them.

We notice that we have 3 and 3^2 as factors in 15 and 18. We'll choose the factor that has the highest exponent. In this case is 3^2.

**lcm [15,18] = 2 * 3^2 * 5 = 90**

Another method would be to write several integers divisible by 15 and several integers divisible by 18.

D15 = 15,30,45,60,75,**90**,105,...

D18 = 18,36,54,72,**90**,108,...

**We notice that the first positive integer divisible by both 15 and 18 is 90. **

To find the LCM or the lowest common multiple, we have to express both the numbers as a product of prime numbers and take the number that we get by multiplying the common prime factors for both.

15 can be written as:

15 = 5 * 3

18 can be written as:

18 = 3 * 3 * 2

Now we see that the common multiples are 5 , 3 , 3 and 2 ( we don't count 3 thrice as counting it twice in the factors of 18 takes care of the 3 in the factors of 15)

So the LCM is 5*3*3*2 = 90.

**The LCM is 90.**