Least Common Multiple (LCM) of 89 and 154
The least common multiple (LCM) of 89 and 154 is 13706.
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 154?
First, calculate the GCD of 89 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 154 = 0 remainder 89 |
| 2 | 154 ÷ 89 = 1 remainder 65 |
| 3 | 89 ÷ 65 = 1 remainder 24 |
| 4 | 65 ÷ 24 = 2 remainder 17 |
| 5 | 24 ÷ 17 = 1 remainder 7 |
| 6 | 17 ÷ 7 = 2 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 27 | 108 |
| 15 and 86 | 1290 |
| 107 and 105 | 11235 |
| 27 and 55 | 1485 |
| 87 and 149 | 12963 |