Least Common Multiple (LCM) of 180 and 118
The least common multiple (LCM) of 180 and 118 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 180 and 118?
First, calculate the GCD of 180 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 118 = 1 remainder 62 |
| 2 | 118 ÷ 62 = 1 remainder 56 |
| 3 | 62 ÷ 56 = 1 remainder 6 |
| 4 | 56 ÷ 6 = 9 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 127 | 13970 |
| 160 and 154 | 12320 |
| 166 and 15 | 2490 |
| 183 and 122 | 366 |
| 105 and 181 | 19005 |