Least Common Multiple (LCM) of 169 and 89
The least common multiple (LCM) of 169 and 89 is 15041.
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 169 and 89?
First, calculate the GCD of 169 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 89 = 1 remainder 80 |
| 2 | 89 ÷ 80 = 1 remainder 9 |
| 3 | 80 ÷ 9 = 8 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 114 | 1824 |
| 132 and 165 | 660 |
| 138 and 54 | 1242 |
| 71 and 172 | 12212 |
| 110 and 194 | 10670 |