Least Common Multiple (LCM) of 117 and 127
The least common multiple (LCM) of 117 and 127 is 14859.
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 117 and 127?
First, calculate the GCD of 117 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 127 = 0 remainder 117 |
| 2 | 127 ÷ 117 = 1 remainder 10 |
| 3 | 117 ÷ 10 = 11 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 134 | 804 |
| 126 and 12 | 252 |
| 144 and 109 | 15696 |
| 54 and 66 | 594 |
| 74 and 144 | 5328 |