Least Common Multiple (LCM) of 69 and 180
The least common multiple (LCM) of 69 and 180 is 4140.
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 180?
First, calculate the GCD of 69 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 180 = 0 remainder 69 |
| 2 | 180 ÷ 69 = 2 remainder 42 |
| 3 | 69 ÷ 42 = 1 remainder 27 |
| 4 | 42 ÷ 27 = 1 remainder 15 |
| 5 | 27 ÷ 15 = 1 remainder 12 |
| 6 | 15 ÷ 12 = 1 remainder 3 |
| 7 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 14 | 1260 |
| 141 and 177 | 8319 |
| 22 and 186 | 2046 |
| 113 and 138 | 15594 |
| 46 and 139 | 6394 |