Least Common Multiple (LCM) of 146 and 69
The least common multiple (LCM) of 146 and 69 is 10074.
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 69?
First, calculate the GCD of 146 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 69 = 2 remainder 8 |
| 2 | 69 ÷ 8 = 8 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 66 | 3432 |
| 60 and 93 | 1860 |
| 193 and 85 | 16405 |
| 96 and 153 | 4896 |
| 85 and 147 | 12495 |