Least Common Multiple (LCM) of 107 and 118
The least common multiple (LCM) of 107 and 118 is 12626.
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 107 and 118?
First, calculate the GCD of 107 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 118 = 0 remainder 107 |
| 2 | 118 ÷ 107 = 1 remainder 11 |
| 3 | 107 ÷ 11 = 9 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 15 | 2310 |
| 115 and 46 | 230 |
| 140 and 16 | 560 |
| 152 and 149 | 22648 |
| 117 and 65 | 585 |