difference between the LCM and HCF of the numbers 20, 30, and 40

Sure, let's calculate the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the numbers 20, 30, and 40.

Step 1: Calculate the HCF The HCF of 20, 30, and 40 can be found by looking at the factors of each number:

• The factors of 20 are: 1, 2, 4, 5, 10, 20
• The factors of 30 are: 1, 2, 3, 5, 10, 15, 30
• The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

The highest number that is a factor of all three numbers is 10, so the HCF is 10.

Step 2: Calculate the LCM The LCM of 20, 30, and 40 can be found by listing the multiples of each number until we find a number that is a multiple of all three:

• The multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240...
• The multiples of 30 are: 30, 60, 90, 120, 150, 180, 210, 240...
• The multiples of 40 are: 40, 80, 120, 160, 200, 240...

The smallest number that is a multiple of all three numbers is 120, so the LCM is 120.

Step 3: Find the difference between the LCM and HCF The difference between the LCM and HCF is: 120 - 10 = 110.