Least Common Multiple (LCM) of 180 and 76
The least common multiple (LCM) of 180 and 76 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 180 and 76?
First, calculate the GCD of 180 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 76 = 2 remainder 28 |
| 2 | 76 ÷ 28 = 2 remainder 20 |
| 3 | 28 ÷ 20 = 1 remainder 8 |
| 4 | 20 ÷ 8 = 2 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 50 | 3950 |
| 107 and 127 | 13589 |
| 101 and 63 | 6363 |
| 143 and 199 | 28457 |
| 10 and 185 | 370 |