Find the LCM by prime factorisation method of 12,15
Answers
Ans 60
Step-by-step 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,
12 into 15 is equal to 180
. 180 is a multiple of both, but is it the least one? Let's look. I start with a prime factorisation of both numbers :
prime factors of 12 are 2 into 2 into 3
prime factors of 15 are 3 into 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:
LCM is equal to 2 into 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
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-- :
Using prime factorisation method:
(i) 12, 15 and 21
Factor of 12=2×2×3
Factor of 15=3×5
Factor of 21=3×7
HCF (12,15,21)=3
LCM (12,15,21)=2×2×3×5×7=420
(ii) 17, 23 and 29
Factor of 17=1×17
Factor of 23=1×23
Factor of 29=1×29
HCF (17,23,29)=1
LCM (17,23,29)=1×17×23×29=11,339
(iii) 8, 9 and 25
Factor of 8=2×2×2×1
Factor of 9=3×3×1
Factor of 25=5×5×1
HCF (8,9,25)=1
LCM (8,9,25)=2×2×2×3×3×5×5=1,800