Least Common Multiple (LCM) of 69 and 149
The least common multiple (LCM) of 69 and 149 is 10281.
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 69 and 149?
First, calculate the GCD of 69 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 149 = 0 remainder 69 |
| 2 | 149 ÷ 69 = 2 remainder 11 |
| 3 | 69 ÷ 11 = 6 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 28 | 2436 |
| 55 and 177 | 9735 |
| 16 and 59 | 944 |
| 72 and 24 | 72 |
| 78 and 195 | 390 |