Least Common Multiple (LCM) of 106 and 117
The least common multiple (LCM) of 106 and 117 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 106 and 117?
First, calculate the GCD of 106 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 117 = 0 remainder 106 |
| 2 | 117 ÷ 106 = 1 remainder 11 |
| 3 | 106 ÷ 11 = 9 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 156 | 1248 |
| 70 and 175 | 350 |
| 180 and 30 | 180 |
| 188 and 27 | 5076 |
| 12 and 14 | 84 |