Least Common Multiple (LCM) of 69 and 133
The least common multiple (LCM) of 69 and 133 is 9177.
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 133?
First, calculate the GCD of 69 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 133 = 0 remainder 69 |
| 2 | 133 ÷ 69 = 1 remainder 64 |
| 3 | 69 ÷ 64 = 1 remainder 5 |
| 4 | 64 ÷ 5 = 12 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 47 | 658 |
| 112 and 39 | 4368 |
| 172 and 148 | 6364 |
| 62 and 45 | 2790 |
| 171 and 31 | 5301 |