lcm help (least comon multiple)?

Question

Find the least common multple (LCM) of each set of numbers of algerbraic expressions

20,12

15,75

24,32

Answer 1

You factor each of the given numbers,

20 - 5 * 2 * 2
12 - 3 * 2 * 2

and then construct a group of numbers so that all the factors are represented. Here, is order to represent two 2s, a 5, and a 3, we need

2 * 2 * 5 * 3, or 60, the least common multiple.

Let's try another.

15 - 5 * 3
75 - 5 * 5 * 3

We need a bunch of numbers that will include two 5s and one 3. The answer is 5 * 5 * 3, or 75.

For the last,

24 - 3 * 2 * 2 * 2
32 - 2 * 2 * 2 * 2 * 2

We need five 2s and a three. That's

2 * 2 * 2 * 2 * 2 * 3, or 96.

Answer 2

20, 12
20 = 2 * 2 * 5
12 - 2 * 2 * 3
so the lcm should be 2 * 2 * 3 * 5 = 60

15, 75
15 = 3 * 5
75 = 3 * 5 * 5
so the lcm is 3 * 5 * 5 = 75 (75 is actually 15 * 5)

24, 32
24 = 2 * 2 * 2 * 3
32 = 2 * 2 * 2 * 2 * 2
so the lcm is 2 * 2 * 2 * 2 * 2 * 3 = 96

Answer 3

20 = 2^2*5
12= 2^2* 3 Lcm 2^2*3*5=60

15=3*5
75=3*5^2 Lcm 3*5^2=75

24=2^3*3
32=2^5 Lcm 2^5*3=96

Answer 4

the least common multiple is the smallest number that matches up when both numbers are multiplied by other numbers, for 20,12 it is 60 because
20x1=20, 20x2=40, and 20x3=60, 20x4=80 and
12x1=12, 12x2=24, 12x3=36, 12x4= 48, 12x5=60, 12x6=72
you see that 20x3=60 and 12x5=60 and no other products before that match, so 60 is the smallest common multiple.

A multiple = the answer to a number times something

Answer 5

2, 3 ,2

Answer 6

60
75
96

Answer 7

60

75

96

Answer 8

60
75
96