Least Common Multiple (LCM) of 111 and 157
The least common multiple (LCM) of 111 and 157 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 111 and 157?
First, calculate the GCD of 111 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 157 = 0 remainder 111 |
| 2 | 157 ÷ 111 = 1 remainder 46 |
| 3 | 111 ÷ 46 = 2 remainder 19 |
| 4 | 46 ÷ 19 = 2 remainder 8 |
| 5 | 19 ÷ 8 = 2 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 112 | 1680 |
| 102 and 53 | 5406 |
| 82 and 186 | 7626 |
| 31 and 37 | 1147 |
| 174 and 23 | 4002 |