Least Common Multiple (LCM) of 126 and 39
The least common multiple (LCM) of 126 and 39 is 1638.
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 39?
First, calculate the GCD of 126 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 39 = 3 remainder 9 |
| 2 | 39 ÷ 9 = 4 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 197 | 7683 |
| 160 and 144 | 1440 |
| 108 and 68 | 1836 |
| 193 and 157 | 30301 |
| 158 and 175 | 27650 |