Least Common Multiple (LCM) of 157 and 89
The least common multiple (LCM) of 157 and 89 is 13973.
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 89?
First, calculate the GCD of 157 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 89 = 1 remainder 68 |
| 2 | 89 ÷ 68 = 1 remainder 21 |
| 3 | 68 ÷ 21 = 3 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 67 | 11591 |
| 89 and 67 | 5963 |
| 168 and 41 | 6888 |
| 136 and 103 | 14008 |
| 74 and 115 | 8510 |