Least Common Multiple (LCM) of 172 and 126
The least common multiple (LCM) of 172 and 126 is 10836.
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 126?
First, calculate the GCD of 172 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 126 = 1 remainder 46 |
| 2 | 126 ÷ 46 = 2 remainder 34 |
| 3 | 46 ÷ 34 = 1 remainder 12 |
| 4 | 34 ÷ 12 = 2 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 146 | 4526 |
| 145 and 118 | 17110 |
| 83 and 24 | 1992 |
| 197 and 70 | 13790 |
| 163 and 165 | 26895 |