Question

Which of the following expressions represents the least common multiple of 15, 18, and 25?

2 · 3 · 5
2 · 3 2 · 5 2
2 · 3 3 · 5 3
2 · 3 2 · 5 3

Answer 1

`(2)(3^2)(5^2)`

Explanation:

we know that

The Least Common Multiple (LCM) of a group of numbers is the smallest number that is a multiple of all the numbers.

we have

15,18 and 25

Decompose the numbers in prime factors

`15=(3)(5)`

`18=(2)(3^2)`

`25=(5^2)`

Multiply common and uncommon numbers with their greatest exponent

so

The LCM is equal to

`LCM=(2)(3^2)(5^2)`

`LCM=450`