If the least common multiple (LCM) of two numbers is 60 and their greatest commo
Practice Questions
Q1
If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
It is 720.
It is 60.
It is 12.
It is 5.
Questions & Step-by-Step Solutions
If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what can be inferred about the product of the two numbers?
Step 1: Understand the terms LCM and GCD. LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers. GCD (Greatest Common Divisor) is the largest number that divides both numbers without leaving a remainder.
Step 2: Note the values given in the question. The LCM is 60 and the GCD is 12.
Step 3: Recall the relationship between the product of two numbers, their LCM, and their GCD. The formula is: Product of the two numbers = LCM * GCD.
Step 4: Substitute the values into the formula. So, we calculate: Product = 60 (LCM) * 12 (GCD).
Step 5: Perform the multiplication: 60 * 12 = 720.
Step 6: Conclude that the product of the two numbers is 720.
Least Common Multiple (LCM) – The smallest multiple that is exactly divisible by two or more numbers.
Greatest Common Divisor (GCD) – The largest positive integer that divides two or more numbers without leaving a remainder.
Relationship between LCM and GCD – The product of two numbers is equal to the product of their LCM and GCD.
