Math Problem Statement

The smallest perfect square which is divisible by 4 and 5 is 300 true or false

Solution

False.

To find the smallest perfect square divisible by both 4 and 5, we need to consider the least common multiple (LCM) of 4 and 5, and then find the smallest perfect square that is a multiple of that LCM.

  1. The LCM of 4 and 5 is 20.
  2. The smallest perfect square that is a multiple of 20 is 20×20=40020 \times 20 = 400.

So, the smallest perfect square divisible by both 4 and 5 is 400, not 300.

Would you like further details or have any questions?

Here are five related questions:

  1. What is the definition of a perfect square?
  2. How do you calculate the least common multiple (LCM) of two numbers?
  3. What is the smallest perfect square divisible by both 3 and 7?
  4. How can you verify if a number is divisible by both 4 and 5?
  5. Can a perfect square ever be an odd number?

Tip: When finding the smallest perfect square divisible by multiple numbers, focus on finding the LCM first and then check if that LCM can be squared.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Number Theory
Perfect Squares
LCM (Least Common Multiple)

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9