Least Common Multiple (LCM) of 18 and 118
The least common multiple (LCM) of 18 and 118 is 1062.
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 18 and 118?
First, calculate the GCD of 18 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 118 = 0 remainder 18 |
| 2 | 118 ÷ 18 = 6 remainder 10 |
| 3 | 18 ÷ 10 = 1 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 35 | 4060 |
| 38 and 79 | 3002 |
| 65 and 59 | 3835 |
| 153 and 151 | 23103 |
| 174 and 106 | 9222 |