Least Common Multiple (LCM) of 109 and 158
The least common multiple (LCM) of 109 and 158 is 17222.
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 158?
First, calculate the GCD of 109 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 158 = 0 remainder 109 |
| 2 | 158 ÷ 109 = 1 remainder 49 |
| 3 | 109 ÷ 49 = 2 remainder 11 |
| 4 | 49 ÷ 11 = 4 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 145 | 5365 |
| 20 and 99 | 1980 |
| 108 and 114 | 2052 |
| 13 and 35 | 455 |
| 189 and 72 | 1512 |