Least Common Multiple (LCM) of 126 and 170
The least common multiple (LCM) of 126 and 170 is 10710.
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 170?
First, calculate the GCD of 126 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 170 = 0 remainder 126 |
| 2 | 170 ÷ 126 = 1 remainder 44 |
| 3 | 126 ÷ 44 = 2 remainder 38 |
| 4 | 44 ÷ 38 = 1 remainder 6 |
| 5 | 38 ÷ 6 = 6 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 27 | 2133 |
| 188 and 32 | 1504 |
| 29 and 172 | 4988 |
| 77 and 153 | 11781 |
| 123 and 137 | 16851 |