Least Common Multiple (LCM) of 89 and 146
The least common multiple (LCM) of 89 and 146 is 12994.
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 146?
First, calculate the GCD of 89 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 146 = 0 remainder 89 |
| 2 | 146 ÷ 89 = 1 remainder 57 |
| 3 | 89 ÷ 57 = 1 remainder 32 |
| 4 | 57 ÷ 32 = 1 remainder 25 |
| 5 | 32 ÷ 25 = 1 remainder 7 |
| 6 | 25 ÷ 7 = 3 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 99 | 10494 |
| 113 and 166 | 18758 |
| 23 and 151 | 3473 |
| 196 and 120 | 5880 |
| 84 and 93 | 2604 |