Least Common Multiple (LCM) of 118 and 180
The least common multiple (LCM) of 118 and 180 is 10620.
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 118 and 180?
First, calculate the GCD of 118 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 180 = 0 remainder 118 |
| 2 | 180 ÷ 118 = 1 remainder 62 |
| 3 | 118 ÷ 62 = 1 remainder 56 |
| 4 | 62 ÷ 56 = 1 remainder 6 |
| 5 | 56 ÷ 6 = 9 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 107 | 2033 |
| 70 and 37 | 2590 |
| 90 and 160 | 1440 |
| 154 and 55 | 770 |
| 90 and 74 | 3330 |