Least Common Multiple (LCM) of 89 and 157
The least common multiple (LCM) of 89 and 157 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 89 and 157?
First, calculate the GCD of 89 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 157 = 0 remainder 89 |
| 2 | 157 ÷ 89 = 1 remainder 68 |
| 3 | 89 ÷ 68 = 1 remainder 21 |
| 4 | 68 ÷ 21 = 3 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 109 | 4251 |
| 82 and 103 | 8446 |
| 88 and 167 | 14696 |
| 77 and 170 | 13090 |
| 192 and 196 | 9408 |