Least Common Multiple (LCM) of 109 and 117
The least common multiple (LCM) of 109 and 117 is 12753.
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 109 and 117?
First, calculate the GCD of 109 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 117 = 0 remainder 109 |
| 2 | 117 ÷ 109 = 1 remainder 8 |
| 3 | 109 ÷ 8 = 13 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 177 | 2124 |
| 194 and 61 | 11834 |
| 169 and 40 | 6760 |
| 76 and 16 | 304 |
| 14 and 127 | 1778 |