Find the least common multiple of 7.2, 1.08 and 21

[Guest]

Find the least common multiple of 7.2, 1.08 and 21

[Guest]

Its 10.08

[adamsmith]

The LCM of 7.2, 1.08 and 21 is 21

[malikadil]

4 . [tex]\frac{7}{8} = \frac{7}{2} = 3.5[/tex]

[Guest]

answer = 756

[john]

L.C.M. for the 3 numbers is 15.12

[Guest]

7.2 x 105 = 756
1.08 x 700 = 756
21 x 36 = 756
so 756 is a common multiple of all the numbers given
and it is the lowest I can find.

[TutorSOS]

(7.2,1.08,21) /2 =(3.6,0.54,21) /2
=(1.8,0.27,21) /3
=(0.6,0.9,7) /3
=0.2,0.3,7
We can’t simplify it, therefore L.C.M.is
2x 2x 3x 3x 0.2x 0.3x 7
=15.12

[Guest]

Find the least common multiple of 7.2, 1.08 and 21
Multiply all by 100 first.

720 = 6, 6, 5, 4

108 = 6, 6, 3

210 = 6, 5, 7

LCM x 100 = 6 x 6 x 5 x 4 x 3 x 7 = 15120
Then real LCM = 151.2

How is that for an answer........






There is an error in the calcs in the last post.....

=(0.6,0.9,7) /3
=0.2,0.3,7

should be....

=(0.6,0.09,7) /3
=0.2,0.03,7

But wouldn't get my answer anyway.....would now give 1.512 ??

[Guest]

Find the least common multiple of 7.2, 1.08 and 21
Multiply all by 100 first.

720 = 6, 6, 5, 4

108 = 6, 6, 3

21 = 3 x 7................should this be mult by 100 ??

2100 = 6 x 7 x 5 x 2 x 5

LCM x 100 = 6 x 6 x 5 x 4 x 3 x 7 x 2 x 5 = 151200
Then real LCM = 1512

which is twice I got in an earlier post....so not least C M ...???

[Guest]

Doing it out again....this time in full with prime factors...then I will hopefully not have any duplicates
I think duplicate 2 in last post...

Find the least common multiple of 7.2, 1.08 and 21
Multiply all by 100 first.

720 = 2^4 x 3^2 x 5

108 = 2^2 x 3^3

2100 = 2^2 x 5^2 x 3 x 7

LCM x100 = 2^4 x 3^3 x 5^2 x 7 = 16 x 27 x 25 x 7 = 75600

So...Real LCM = 756 .......as I had got in an earlier post.......

Check........
7.2 x 105 = 756
1.08 x 700 = 756
21 x 36 = 756
.... so as can be seen .... 756 is a multiple of all the numbers given...........

[leesajohnson]

It's 756 the multiplication all the numbers were given.

[Guest]

163.296 is the multiplication of the numbers given

[Guest]

Lowest common multiple satisfies the property
Lcm(ab,ac) = a Lcm(b,c)
which implies Lcm(ab,ac,ad) = a Lcm(b,c,d)

So Lcm(7.2,1.08,21) = Lcm(720,108,2100)/100 = 75600/100 = 756

Alternatively (and equivalently) look at the prime factorization (allowing for negative exponents) and take the maximum exponent for each prime
[tex]7.2 = 72/10 = 2^2\times 3^2\times 5^{-1}[/tex]
[tex]1.08 = 108/100 = 3^3\times 5^{-2}[/tex]
[tex]21 = 3^1\times 7^1[/tex] (note that the exponent of 5 is 0)
Lcm has the maximum exponent for each prime factor = [tex]2^2\times 3^3\times 5^0 \times 7^1\times 11^0\times 13^0\times\ldots = 756[/tex].

Hope this helped,

R. Baber.

[Guest]

Frankly, I don't know how this has gone on so long. "Least Common Multiple" is usually defined for positive integers because if we allow fractions ANY number is a multiple of any other!

[Guest]

Hey! I used an https://www.meracalculator.com/math/lcm.php by Meracalculater.com and it shows me steps here. PS it removes the decimal and you can understand through the steps.
It shows the LCM is "1512"

[Guest]

Finding the Least Common Multiple is not hard. Lcm can be calculated by more than two integers or fractions. And there are several methods you can use. For example Long Division Method, Brute Force Method, Prime Factorization Method. I hope this helps somewhere

[Angus53]

To find the least common multiple (LCM) of 7.2, 1.08, and 21, first, express them as integers by multiplying each number by 100 (to remove decimals):

7.2 * 100 = 720
1.08 * 100 = 108

Now, we have 720, 108, and 21.

The prime factorization of these numbers are:
720 = 2^4 * 3^2 * 5
108 = 2^2 * 3^3
21 = 3 * 7

Now, identify the highest power of each prime factor:
- 2^4
- 3^3
- 5
- 7

Now, multiply these highest powers together to find the LCM:
LCM = 2^4 * 3^3 * 5 * 7 = 16 * 27 * 5 * 7 = 8,640

So, the least common multiple of 7.2, 1.08, and 21 is 8,640.