Least Common Multiple (LCM) of 117 and 67
The least common multiple (LCM) of 117 and 67 is 7839.
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 67?
First, calculate the GCD of 117 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 67 = 1 remainder 50 |
| 2 | 67 ÷ 50 = 1 remainder 17 |
| 3 | 50 ÷ 17 = 2 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 66 | 2310 |
| 53 and 169 | 8957 |
| 176 and 199 | 35024 |
| 31 and 12 | 372 |
| 36 and 167 | 6012 |