Least Common Multiple (LCM) of 38 and 180
The least common multiple (LCM) of 38 and 180 is 3420.
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 38 and 180?
First, calculate the GCD of 38 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 180 = 0 remainder 38 |
| 2 | 180 ÷ 38 = 4 remainder 28 |
| 3 | 38 ÷ 28 = 1 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 72 | 2520 |
| 30 and 24 | 120 |
| 68 and 151 | 10268 |
| 120 and 90 | 360 |
| 110 and 146 | 8030 |