3411. Maximum Subarray With Equal Products

You are given an array of positive integers nums.

An array arr is called product equivalent if prod(arr) == lcm(arr) * gcd(arr), where:

• prod(arr) is the product of all elements of arr.
• gcd(arr) is the GCD of all elements of arr.
• lcm(arr) is the LCM of all elements of arr.

Return the length of the longest product equivalent subarray of nums.

Constraints:

• 2 <= nums.length <= 100
• 1 <= nums[i] <= 10

GCD (Greatest Common Divisor) means the largest number that can divide both numbers without leaving a remainder.

For example:

GCD of 12 and 18 is 6 because 6 is the largest number that can divide both 12 and 18 exactly (12 ÷ 6 = 2, 18 ÷ 6 = 3).

In python, we can use these two methods for getting gcd of 2 numbers:

def gcd(a, b):


  while b:


    a, b = b, a % b


  return a

def gcd(a, b):

return math.gcd(a, b)

LCM (Least Common Multiple) means the smallest positive number that is a multiple of both numbers.

For example:

LCM of 12 and 18 is 36, because:
36 is divisible by both 12 and 18.
It is the smallest number that satisfies this condition.

Relationship Between GCD and LCM:
lcm(a, b) = abs(a * b) / gcd(a, b)



class Solution:
def maxLength(self, nums: List[int]) -> int:
n = len(nums)
ans = 1
for i in range(n):
p = nums[i]
g = nums[i]
l = nums[i]
for j in range(i + 1, n):
p *= nums[j]
g = math.gcd(g, nums[j])
l = self.lcm(l, nums[j])
if l * g == p:
ans = max(ans, j - i + 1)
return ans

def lcm(self, a, b):
return abs(a * b) // math.gcd(a, b)