Least Common Multiple (LCM) of 114 and 157
The least common multiple (LCM) of 114 and 157 is 17898.
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 114 and 157?
First, calculate the GCD of 114 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 157 = 0 remainder 114 |
| 2 | 157 ÷ 114 = 1 remainder 43 |
| 3 | 114 ÷ 43 = 2 remainder 28 |
| 4 | 43 ÷ 28 = 1 remainder 15 |
| 5 | 28 ÷ 15 = 1 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 167 | 25384 |
| 40 and 192 | 960 |
| 102 and 38 | 1938 |
| 143 and 64 | 9152 |
| 100 and 97 | 9700 |