Least Common Multiple (LCM) of 16 and 73
The least common multiple (LCM) of 16 and 73 is 1168.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 16 and 73?
First, calculate the GCD of 16 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 73 = 0 remainder 16 |
| 2 | 73 ÷ 16 = 4 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 73 | 7519 |
| 150 and 133 | 19950 |
| 124 and 41 | 5084 |
| 167 and 167 | 167 |
| 104 and 150 | 7800 |