Least Common Multiple (LCM) of 126 and 69
The least common multiple (LCM) of 126 and 69 is 2898.
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 69?
First, calculate the GCD of 126 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 69 = 1 remainder 57 |
| 2 | 69 ÷ 57 = 1 remainder 12 |
| 3 | 57 ÷ 12 = 4 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 63 | 1386 |
| 68 and 64 | 1088 |
| 122 and 93 | 11346 |
| 51 and 197 | 10047 |
| 104 and 143 | 1144 |