Question

Find the LCM of the following number by division method.
a. 30,60 and 240​

Answer 1

240

Explanation:

Answer 2

240

Explanation:

You want the least common multiple of 30, 60, and 240 by the division method.

Common divisors

First, we'll look for common divisors. We notice all the numbers are even, so we start with 2:

`\begin{array}c2&30&60&240\\3&15&30&120\\5&5&10&40\\2&1&2&8\\&-&1&4\end{array}`

The remaining "uncommon" divisor, 4, is not prime, but any additional divisors put in the left column will have that as their product.

LCM

The LCM is the product of the common divisors and the remaining uncommon divisors:

(2)(3)(5)(2)(4) = 240

The LCM of 30, 60, 240 is 240.

__

Additional comment

If you're paying attention, you know that 30 and 60 are divisors of 240, so 240 is the LCM of these numbers.

The division method lists prime divisors down the left column, and the result of division by that on the next row. When a row is all prime numbers, you're done. Or, as here, when there is only one number in the row that is greater than 1, you're done. When a column ends in 1, it is removed from further consideration.

<95141404393>