Least Common Multiple (LCM) of 126 and 55
The least common multiple (LCM) of 126 and 55 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 126 and 55?
First, calculate the GCD of 126 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 55 = 2 remainder 16 |
| 2 | 55 ÷ 16 = 3 remainder 7 |
| 3 | 16 ÷ 7 = 2 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 122 | 17690 |
| 178 and 18 | 1602 |
| 135 and 130 | 3510 |
| 171 and 74 | 12654 |
| 39 and 78 | 78 |