Least Common Multiple (LCM) of 180 and 105
The least common multiple (LCM) of 180 and 105 is 1260.
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 105?
First, calculate the GCD of 180 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 105 = 1 remainder 75 |
| 2 | 105 ÷ 75 = 1 remainder 30 |
| 3 | 75 ÷ 30 = 2 remainder 15 |
| 4 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 15 | 795 |
| 175 and 187 | 32725 |
| 190 and 61 | 11590 |
| 137 and 31 | 4247 |
| 21 and 68 | 1428 |