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 |
|---|---|
| 173 and 72 | 12456 |
| 100 and 126 | 6300 |
| 107 and 66 | 7062 |
| 106 and 165 | 17490 |
| 96 and 32 | 96 |