Least Common Multiple (LCM) of 117 and 106
The least common multiple (LCM) of 117 and 106 is 12402.
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 106?
First, calculate the GCD of 117 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 106 = 1 remainder 11 |
| 2 | 106 ÷ 11 = 9 remainder 7 |
| 3 | 11 ÷ 7 = 1 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 193 | 193 |
| 41 and 69 | 2829 |
| 112 and 57 | 6384 |
| 141 and 179 | 25239 |
| 25 and 134 | 3350 |