Least Common Multiple (LCM) of 126 and 167
The least common multiple (LCM) of 126 and 167 is 21042.
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 167?
First, calculate the GCD of 126 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 167 = 0 remainder 126 |
| 2 | 167 ÷ 126 = 1 remainder 41 |
| 3 | 126 ÷ 41 = 3 remainder 3 |
| 4 | 41 ÷ 3 = 13 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 142 | 710 |
| 107 and 147 | 15729 |
| 59 and 177 | 177 |
| 45 and 157 | 7065 |
| 81 and 42 | 1134 |