Least Common Multiple (LCM) of 126 and 79
The least common multiple (LCM) of 126 and 79 is 9954.
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 79?
First, calculate the GCD of 126 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 79 = 1 remainder 47 |
| 2 | 79 ÷ 47 = 1 remainder 32 |
| 3 | 47 ÷ 32 = 1 remainder 15 |
| 4 | 32 ÷ 15 = 2 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 172 | 3612 |
| 99 and 174 | 5742 |
| 51 and 38 | 1938 |
| 189 and 42 | 378 |
| 12 and 174 | 348 |