find the LCM of the following number by listing multiples of 12 and 15
Answers
Answer:
Step-by-step explanation:
please mark as brainlist
Answer:
L
C
M
=
60
Explanation:
When we're looking at the LCM (Least Common Multiple), we're looking for a number that both 12 and 15 are a factor of. Oftentimes people simply assume that if we multiply the two together, we'll find it. In this case, it'd be
12
×
15
=
180
. 180 is a multiple of both, but is it the least one? Let's look.
I start with a prime factorization of both numbers:
12
=
2
×
2
×
3
15
=
3
×
5
To find the LCM, we want to have all the prime factors from both numbers accounted for.
For instance, there are two 2s (in the 12). Let's put those in:
L
C
M
=
2
×
2
×
...
There is one 3 in both the 12 and the 15, so we need one 3:
L
C
M
=
2
×
2
×
3
×
...
And there is one 5 (in the 15) so let's put that in:
L
C
M
=
2
×
2
×
3
×
5
=
60
12
×
5
=
60
15
×
3
=
60
Answer:
60
Explanation:
another approach is to use teh relation
a
b
=
h
c
f
(
a
,
b
)
lcm
(
a
b
)
now
h
c
f
(
12
,
15
)
=
3
∴
12
×
15
=
3
×
lcm
(
12
,
15
)
lcm
(
12
,
15
)
=
12
4
×
15
3
lcm
=
4
×
15
=
60