Least Common Multiple (LCM) of 89 and 136
The least common multiple (LCM) of 89 and 136 is 12104.
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 136?
First, calculate the GCD of 89 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 136 = 0 remainder 89 |
| 2 | 136 ÷ 89 = 1 remainder 47 |
| 3 | 89 ÷ 47 = 1 remainder 42 |
| 4 | 47 ÷ 42 = 1 remainder 5 |
| 5 | 42 ÷ 5 = 8 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 75 | 1950 |
| 53 and 105 | 5565 |
| 102 and 116 | 5916 |
| 194 and 10 | 970 |
| 156 and 147 | 7644 |