Least Common Multiple (LCM) of 72 and 16
The least common multiple (LCM) of 72 and 16 is 144.
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 72 and 16?
First, calculate the GCD of 72 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 16 = 4 remainder 8 |
| 2 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 81 | 14175 |
| 102 and 51 | 102 |
| 107 and 164 | 17548 |
| 193 and 196 | 37828 |
| 106 and 159 | 318 |