Least Common Multiple (LCM) of 157 and 111
The least common multiple (LCM) of 157 and 111 is 17427.
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 111?
First, calculate the GCD of 157 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 111 = 1 remainder 46 |
| 2 | 111 ÷ 46 = 2 remainder 19 |
| 3 | 46 ÷ 19 = 2 remainder 8 |
| 4 | 19 ÷ 8 = 2 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 55 | 10615 |
| 55 and 157 | 8635 |
| 49 and 133 | 931 |
| 82 and 58 | 2378 |
| 134 and 133 | 17822 |