Least Common Multiple (LCM) of 22 and 118
The least common multiple (LCM) of 22 and 118 is 1298.
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 22 and 118?
First, calculate the GCD of 22 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 118 = 0 remainder 22 |
| 2 | 118 ÷ 22 = 5 remainder 8 |
| 3 | 22 ÷ 8 = 2 remainder 6 |
| 4 | 8 ÷ 6 = 1 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 37 | 111 |
| 39 and 53 | 2067 |
| 128 and 180 | 5760 |
| 137 and 92 | 12604 |
| 122 and 198 | 12078 |