If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
Practice Questions
1 question
Q1
If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
720
180
120
60
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Questions & Step-by-step Solutions
1 item
Q
Q: If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
Solution: The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Steps: 6
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: Identify the values given in the question. The LCM is 60 and the GCD is 12.
Step 3: Use the formula that relates the product of two numbers to their LCM and GCD. The formula is: Product of two numbers = LCM * GCD.
Step 4: Substitute the values into the formula. So, we calculate: 60 (LCM) * 12 (GCD).
Step 5: Perform the multiplication: 60 * 12 = 720.
Step 6: Conclude that the product of the two numbers is 720.
