Least Common Multiple (LCM) of 156 and 193
The least common multiple (LCM) of 156 and 193 is 30108.
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 156 and 193?
First, calculate the GCD of 156 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 193 = 0 remainder 156 |
| 2 | 193 ÷ 156 = 1 remainder 37 |
| 3 | 156 ÷ 37 = 4 remainder 8 |
| 4 | 37 ÷ 8 = 4 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 104 | 8216 |
| 131 and 59 | 7729 |
| 197 and 156 | 30732 |
| 160 and 188 | 7520 |
| 133 and 107 | 14231 |