Least Common Multiple (LCM) of 67 and 107
The least common multiple (LCM) of 67 and 107 is 7169.
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 107?
First, calculate the GCD of 67 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 107 = 0 remainder 67 |
| 2 | 107 ÷ 67 = 1 remainder 40 |
| 3 | 67 ÷ 40 = 1 remainder 27 |
| 4 | 40 ÷ 27 = 1 remainder 13 |
| 5 | 27 ÷ 13 = 2 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 133 | 2261 |
| 48 and 41 | 1968 |
| 115 and 129 | 14835 |
| 29 and 108 | 3132 |
| 143 and 15 | 2145 |