What is the LCM of 184 and 84?

Answer 1

Since 184 is a multiple of 23, the answer is 184. 23x8 is 184.

It is never a bad idea when looking for the LCM of 2 number and one is much bigger to see if the smaller number goes into the bigger one evenly. If so, you are done!

Answer 2

Writing down the multiples of both 184 and 84 and then finding the common multiple is tedious.

Method of prime factorization is much better to find LCM.

First of all we express each number as the product of prime numbers.

Prime factorization of 184 = 2 x 2 x 2 x 23 = 23 x 231

Two distinct prime factors: 2 and 23

Prime factorization of 84 = 2 x 2 x 3 x 7 = 22 x 31 x 71

Three distinct prime factors: 2, 3 and 7

Product of prime factors to the highest powers in each category gives LCM.

Highest power of 2 is 3.

Highest power of 23 is 1.

Highest power of 3 is 1.

Highest power of 7 is 1.

So, LCM is 23 x 231 x 31 x 71 = 3864.

In depth:

Any common multiple of 184 and 84 must have 2 x 2 x 2 x 23(184) and 2 x 2 x 3 x 7(84) in its prime factorization.

Since 184 has more 2s in its prime factorization so 84 can share its 2s. So we can reject 2s of 84. Whereas 23, 7 and 3 are not common in the prime factorization so they will remain as it is.

So, LCM(184, 84) = 23 x 231 x 31 x 71 = 23 x 231 x 31 x 71 = 184 x 31 x 71.

And LCM(184, 84) = 22 x 31 x 71 x 21 x 231 = 84 x 21 x 231(it can be seen here how 84 shares the 2s of 184).

Answer 3

The LCM is: 1,471,382

Answer 4

The LCM is 3864.