Is the statement below sometimes, always, or never true? give at least two examples to support your reasoning. the lcm of two square numbers is another square number.

Always true.

Step-by-step explanation:

A squared number will always have paired prime factors. When they have no prime factors in common, like 4 (2 x 2) and 9 (3 x 3), the LCM will be their product, 2 x 2 x 3 x 3 or 36 (6 squared). When they have prime factors in common, like 36 (2 x 2 x 3 x 3) and 225 (3 x 3 x 5 x 5), the LCM will still have paired factors: 2 x 2 x 3 x 3 x 5 x 5 or 900 (30 squared)

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

the answer is b