Least Common Multiple (LCM) of 55 and 126
The least common multiple (LCM) of 55 and 126 is 6930.
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 55 and 126?
First, calculate the GCD of 55 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 126 = 0 remainder 55 |
| 2 | 126 ÷ 55 = 2 remainder 16 |
| 3 | 55 ÷ 16 = 3 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 45 | 495 |
| 78 and 137 | 10686 |
| 177 and 164 | 29028 |
| 90 and 169 | 15210 |
| 93 and 138 | 4278 |