Least Common Multiple (LCM) of 70 and 180
The least common multiple (LCM) of 70 and 180 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 70 and 180?
First, calculate the GCD of 70 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 180 = 0 remainder 70 |
| 2 | 180 ÷ 70 = 2 remainder 40 |
| 3 | 70 ÷ 40 = 1 remainder 30 |
| 4 | 40 ÷ 30 = 1 remainder 10 |
| 5 | 30 ÷ 10 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 187 | 19635 |
| 77 and 94 | 7238 |
| 109 and 106 | 11554 |
| 180 and 130 | 2340 |
| 10 and 186 | 930 |