What is the LCM of 36, 8, 72, 12?

Question

iluvyou23452nwj · Accepted Answer

Step 1
You can find the LCM and HCF of any set of numbers by breaking each one down into the product of its ' factors:
$36 = 2 \times 2 \times 3 \times 3$
$8 = 2 \times 2 \times 2$
$72 = 2 \times 2 \times 2 \times 3 \times 3$
$12 = \underset{―}{2 \times 2 \times 3}$
LCM $= 2 \times 2 \times 2 \times 3 \times 3$
The LCM must contain all the ' factors of all the numbers, but without unnecessary duplicates.
Both 8 and 72 have $2^{3}$
Both 36 and 72 have $3^{2}$
But we only need $2^{3}$ and $3^{2}$ to include all the numbers.

bijteny85 · Accepted Answer

Step 1
So LCM means the lowest common multiple which in other words means what is the smallest number that is divisible by all the numbers you have present.
ie what is the smallest number which can be divided by 36, 8, 72 and 12 without any remainders?
So looking at the multiples of all the numbers you have
multiples of

36 : 36, 72, 108, \dots

multiples of

8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, \dots

multiples of

72 : 72, 144, 216, \dots

multiples of

12 : 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, \dots

From above, you can clearly see that

72

is the answer because it is the first common number that you can find in each of the multiples of 36, 8, 72 and 12.

What is the LCM of 36, 8, 72, 12?

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