Least Common Multiple (LCM) of 69 and 156
The least common multiple (LCM) of 69 and 156 is 3588.
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 156?
First, calculate the GCD of 69 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 156 = 0 remainder 69 |
| 2 | 156 ÷ 69 = 2 remainder 18 |
| 3 | 69 ÷ 18 = 3 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 57 | 3648 |
| 44 and 50 | 1100 |
| 82 and 200 | 8200 |
| 72 and 40 | 360 |
| 105 and 81 | 2835 |