Least Common Multiple (LCM) of 141 and 180
The least common multiple (LCM) of 141 and 180 is 8460.
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 141 and 180?
First, calculate the GCD of 141 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 141 ÷ 180 = 0 remainder 141 |
| 2 | 180 ÷ 141 = 1 remainder 39 |
| 3 | 141 ÷ 39 = 3 remainder 24 |
| 4 | 39 ÷ 24 = 1 remainder 15 |
| 5 | 24 ÷ 15 = 1 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 106 | 8692 |
| 92 and 164 | 3772 |
| 180 and 169 | 30420 |
| 116 and 71 | 8236 |
| 173 and 95 | 16435 |