Least Common Multiple (LCM) of 76 and 180
The least common multiple (LCM) of 76 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 76 and 180?
First, calculate the GCD of 76 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 180 = 0 remainder 76 |
| 2 | 180 ÷ 76 = 2 remainder 28 |
| 3 | 76 ÷ 28 = 2 remainder 20 |
| 4 | 28 ÷ 20 = 1 remainder 8 |
| 5 | 20 ÷ 8 = 2 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 80 | 5520 |
| 137 and 137 | 137 |
| 125 and 25 | 125 |
| 88 and 23 | 2024 |
| 96 and 32 | 96 |