Least Common Multiple (LCM) of 180 and 141
The least common multiple (LCM) of 180 and 141 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 180 and 141?
First, calculate the GCD of 180 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 141 = 1 remainder 39 |
| 2 | 141 ÷ 39 = 3 remainder 24 |
| 3 | 39 ÷ 24 = 1 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 58 | 4466 |
| 48 and 92 | 1104 |
| 84 and 103 | 8652 |
| 108 and 130 | 7020 |
| 30 and 132 | 660 |