Least Common Multiple (LCM) of 117 and 34
The least common multiple (LCM) of 117 and 34 is 3978.
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 34?
First, calculate the GCD of 117 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 34 = 3 remainder 15 |
| 2 | 34 ÷ 15 = 2 remainder 4 |
| 3 | 15 ÷ 4 = 3 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 130 | 2730 |
| 89 and 137 | 12193 |
| 39 and 96 | 1248 |
| 155 and 41 | 6355 |
| 167 and 42 | 7014 |