Least Common Multiple (LCM) of 109 and 187
The least common multiple (LCM) of 109 and 187 is 20383.
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 187?
First, calculate the GCD of 109 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 187 = 0 remainder 109 |
| 2 | 187 ÷ 109 = 1 remainder 78 |
| 3 | 109 ÷ 78 = 1 remainder 31 |
| 4 | 78 ÷ 31 = 2 remainder 16 |
| 5 | 31 ÷ 16 = 1 remainder 15 |
| 6 | 16 ÷ 15 = 1 remainder 1 |
| 7 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 32 | 1632 |
| 89 and 67 | 5963 |
| 135 and 112 | 15120 |
| 45 and 62 | 2790 |
| 100 and 99 | 9900 |