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

Question

Charles Benedict · Accepted Answer

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
multiplies of

36 : 36, 72, 108, \dots

multiplies of

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

multiplies of

72 : 72, 144, 216, \dots

multiplies 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

.

boronganfh · Accepted Answer

You can find the LCM and HC of any set of numbers by breaking each one down into the product of its prime 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 = 2 \times 2 \times 3

L C M = 2 \times 2 \times 2 \times 3 \times 3

The LCM must contain all the prime 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.

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

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