Least Common Multiple (LCM) of 157 and 188
The least common multiple (LCM) of 157 and 188 is 29516.
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 188?
First, calculate the GCD of 157 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 188 = 0 remainder 157 |
| 2 | 188 ÷ 157 = 1 remainder 31 |
| 3 | 157 ÷ 31 = 5 remainder 2 |
| 4 | 31 ÷ 2 = 15 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 67 | 2211 |
| 111 and 165 | 6105 |
| 153 and 27 | 459 |
| 69 and 199 | 13731 |
| 17 and 23 | 391 |