Least Common Multiple (LCM) of 72 and 199
The least common multiple (LCM) of 72 and 199 is 14328.
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 199?
First, calculate the GCD of 72 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 199 = 0 remainder 72 |
| 2 | 199 ÷ 72 = 2 remainder 55 |
| 3 | 72 ÷ 55 = 1 remainder 17 |
| 4 | 55 ÷ 17 = 3 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 27 | 1728 |
| 197 and 46 | 9062 |
| 137 and 160 | 21920 |
| 160 and 131 | 20960 |
| 189 and 161 | 4347 |