Least Common Multiple (LCM) of 146 and 169
The least common multiple (LCM) of 146 and 169 is 24674.
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 146 and 169?
First, calculate the GCD of 146 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 169 = 0 remainder 146 |
| 2 | 169 ÷ 146 = 1 remainder 23 |
| 3 | 146 ÷ 23 = 6 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 197 | 35460 |
| 43 and 128 | 5504 |
| 100 and 185 | 3700 |
| 164 and 141 | 23124 |
| 88 and 23 | 2024 |