Least Common Multiple (LCM) of 180 and 59
The least common multiple (LCM) of 180 and 59 is 10620.
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 59?
First, calculate the GCD of 180 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 59 = 3 remainder 3 |
| 2 | 59 ÷ 3 = 19 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 162 | 3564 |
| 159 and 199 | 31641 |
| 72 and 114 | 1368 |
| 107 and 92 | 9844 |
| 49 and 60 | 2940 |