Least Common Multiple (LCM) of 157 and 193
The least common multiple (LCM) of 157 and 193 is 30301.
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 157 and 193?
First, calculate the GCD of 157 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 193 = 0 remainder 157 |
| 2 | 193 ÷ 157 = 1 remainder 36 |
| 3 | 157 ÷ 36 = 4 remainder 13 |
| 4 | 36 ÷ 13 = 2 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 195 | 19110 |
| 120 and 172 | 5160 |
| 109 and 94 | 10246 |
| 56 and 116 | 1624 |
| 69 and 54 | 1242 |