Least Common Multiple (LCM) of 172 and 83
The least common multiple (LCM) of 172 and 83 is 14276.
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 172 and 83?
First, calculate the GCD of 172 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 83 = 2 remainder 6 |
| 2 | 83 ÷ 6 = 13 remainder 5 |
| 3 | 6 ÷ 5 = 1 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 198 | 5742 |
| 165 and 147 | 8085 |
| 188 and 119 | 22372 |
| 49 and 69 | 3381 |
| 119 and 162 | 19278 |