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

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hala718's profile pic

Posted on

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

neela's profile pic

Posted on

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.

giorgiana1976's profile pic

Posted on

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. 

william1941's profile pic

Posted on

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.

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