Least Common Multiple (LCM) of 67 and 117
The least common multiple (LCM) of 67 and 117 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 67 and 117?
First, calculate the GCD of 67 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 117 = 0 remainder 67 |
| 2 | 117 ÷ 67 = 1 remainder 50 |
| 3 | 67 ÷ 50 = 1 remainder 17 |
| 4 | 50 ÷ 17 = 2 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 10 | 60 |
| 132 and 16 | 528 |
| 109 and 103 | 11227 |
| 89 and 147 | 13083 |
| 128 and 26 | 1664 |