Least Common Multiple (LCM) of 20 and 118
The least common multiple (LCM) of 20 and 118 is 1180.
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 20 and 118?
First, calculate the GCD of 20 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 118 = 0 remainder 20 |
| 2 | 118 ÷ 20 = 5 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 152 | 4104 |
| 105 and 75 | 525 |
| 85 and 113 | 9605 |
| 22 and 59 | 1298 |
| 90 and 180 | 180 |