Least Common Multiple (LCM) of 117 and 38
The least common multiple (LCM) of 117 and 38 is 4446.
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 38?
First, calculate the GCD of 117 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 38 = 3 remainder 3 |
| 2 | 38 ÷ 3 = 12 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 156 | 27924 |
| 21 and 47 | 987 |
| 67 and 134 | 134 |
| 68 and 149 | 10132 |
| 180 and 105 | 1260 |