Least Common Multiple (LCM) of 180 and 123
The least common multiple (LCM) of 180 and 123 is 7380.
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 123?
First, calculate the GCD of 180 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 123 = 1 remainder 57 |
| 2 | 123 ÷ 57 = 2 remainder 9 |
| 3 | 57 ÷ 9 = 6 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 150 | 4350 |
| 87 and 68 | 5916 |
| 33 and 74 | 2442 |
| 91 and 83 | 7553 |
| 10 and 151 | 1510 |