Can 72 and 20 respectively be the LCM and HCF of two numbers? Give reason.
The LCM of two or more numbers is the smallest number among all common multiples of the given numbers. The HCF of two or more numbers is the highest number among all the common factors of the given numbers.
Answer: No, 72 and 20 cannot be the LCM and HCF of two numbers because when 72 is divided by 20, it leaves a remainder of 12.
Let's find whether 72 and 20 are the LCM and HCF of two numbers or not.
The LCM of two numbers is exactly divisible by the HCF of the numbers.
But, when 72 is divided by 20, it gives a quotient of 3 and a remainder of 12.
Therefore, 72 is not exactly divisible by 20.
So, 20 and 72 cannot be the HCF & LCM of two numbers.