Least Common Multiple (LCM) of 154 and 193
The least common multiple (LCM) of 154 and 193 is 29722.
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 154 and 193?
First, calculate the GCD of 154 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 193 = 0 remainder 154 |
| 2 | 193 ÷ 154 = 1 remainder 39 |
| 3 | 154 ÷ 39 = 3 remainder 37 |
| 4 | 39 ÷ 37 = 1 remainder 2 |
| 5 | 37 ÷ 2 = 18 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 84 | 672 |
| 13 and 169 | 169 |
| 197 and 143 | 28171 |
| 175 and 17 | 2975 |
| 19 and 80 | 1520 |