Least Common Multiple (LCM) of 157 and 192
The least common multiple (LCM) of 157 and 192 is 30144.
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 192?
First, calculate the GCD of 157 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 192 = 0 remainder 157 |
| 2 | 192 ÷ 157 = 1 remainder 35 |
| 3 | 157 ÷ 35 = 4 remainder 17 |
| 4 | 35 ÷ 17 = 2 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 109 | 11554 |
| 17 and 51 | 51 |
| 20 and 161 | 3220 |
| 79 and 123 | 9717 |
| 40 and 83 | 3320 |