Least Common Multiple (LCM) of 117 and 22
The least common multiple (LCM) of 117 and 22 is 2574.
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 117 and 22?
First, calculate the GCD of 117 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 22 = 5 remainder 7 |
| 2 | 22 ÷ 7 = 3 remainder 1 |
| 3 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 123 | 14268 |
| 122 and 11 | 1342 |
| 25 and 87 | 2175 |
| 175 and 97 | 16975 |
| 47 and 80 | 3760 |