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

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eligia | Student, College Freshman | eNoter

Posted October 5, 2010 at 2:12 AM via web

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

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giorgiana1976 | College Teacher | Valedictorian

Posted October 5, 2010 at 2:14 AM (Answer #1)

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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. 

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted October 5, 2010 at 2:21 AM (Answer #2)

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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

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neela | High School Teacher | Valedictorian

Posted October 5, 2010 at 2:39 AM (Answer #3)

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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.

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william1941 | College Teacher | Valedictorian

Posted October 5, 2010 at 2:26 AM (Answer #4)

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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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