Least Common Multiple (LCM) of 126 and 172
The least common multiple (LCM) of 126 and 172 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 126 and 172?
First, calculate the GCD of 126 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 172 = 0 remainder 126 |
| 2 | 172 ÷ 126 = 1 remainder 46 |
| 3 | 126 ÷ 46 = 2 remainder 34 |
| 4 | 46 ÷ 34 = 1 remainder 12 |
| 5 | 34 ÷ 12 = 2 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 184 | 2760 |
| 43 and 30 | 1290 |
| 172 and 47 | 8084 |
| 28 and 173 | 4844 |
| 40 and 74 | 1480 |